Properties

Label 5040.2.a
Level $5040$
Weight $2$
Character orbit 5040.a
Rep. character $\chi_{5040}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $51$
Sturm bound $2304$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5040.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 51 \)
Sturm bound: \(2304\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5040))\).

Total New Old
Modular forms 1200 60 1140
Cusp forms 1105 60 1045
Eisenstein series 95 0 95

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)\(7\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(27\)
Minus space\(-\)\(33\)

Trace form

\( 60 q + 2 q^{7} + 4 q^{11} - 8 q^{17} - 8 q^{19} - 8 q^{23} + 60 q^{25} - 8 q^{29} - 8 q^{31} + 6 q^{35} - 8 q^{37} + 8 q^{41} - 8 q^{43} - 24 q^{47} + 60 q^{49} - 8 q^{53} - 48 q^{59} + 16 q^{61} - 8 q^{67}+ \cdots + 40 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5040))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 5 7
5040.2.a.a 5040.a 1.a $1$ $40.245$ \(\Q\) None 280.2.a.a \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-5q^{11}-5q^{13}+7q^{17}+\cdots\)
5040.2.a.b 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.h \(0\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-2q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.c 5040.a 1.a $1$ $40.245$ \(\Q\) None 420.2.a.b \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.d 5040.a 1.a $1$ $40.245$ \(\Q\) None 105.2.a.a \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-6q^{13}-2q^{17}+8q^{19}+\cdots\)
5040.2.a.e 5040.a 1.a $1$ $40.245$ \(\Q\) None 1260.2.a.d \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-4q^{13}-6q^{17}-2q^{19}+\cdots\)
5040.2.a.f 5040.a 1.a $1$ $40.245$ \(\Q\) None 630.2.a.c \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.g 5040.a 1.a $1$ $40.245$ \(\Q\) None 210.2.a.b \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{13}+6q^{17}-8q^{19}+\cdots\)
5040.2.a.h 5040.a 1.a $1$ $40.245$ \(\Q\) None 140.2.a.a \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+3q^{11}-q^{13}+3q^{17}+\cdots\)
5040.2.a.i 5040.a 1.a $1$ $40.245$ \(\Q\) None 210.2.a.c \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.j 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.f \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.k 5040.a 1.a $1$ $40.245$ \(\Q\) None 210.2.a.e \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.l 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.d \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.m 5040.a 1.a $1$ $40.245$ \(\Q\) None 1260.2.a.b \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}+2q^{17}+6q^{19}+\cdots\)
5040.2.a.n 5040.a 1.a $1$ $40.245$ \(\Q\) None 630.2.a.e \(0\) \(0\) \(-1\) \(1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.o 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.e \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-2q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.p 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.e \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+2q^{13}-2q^{17}+q^{25}+\cdots\)
5040.2.a.q 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.c \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+2q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.r 5040.a 1.a $1$ $40.245$ \(\Q\) None 420.2.a.d \(0\) \(0\) \(-1\) \(1\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
5040.2.a.s 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.j \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
5040.2.a.t 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.b \(0\) \(0\) \(-1\) \(1\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.u 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.b \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
5040.2.a.v 5040.a 1.a $1$ $40.245$ \(\Q\) None 35.2.a.a \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-3q^{11}+5q^{13}-3q^{17}+\cdots\)
5040.2.a.w 5040.a 1.a $1$ $40.245$ \(\Q\) None 1260.2.a.d \(0\) \(0\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-4q^{13}+6q^{17}-2q^{19}+\cdots\)
5040.2.a.x 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.c \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{13}-6q^{17}+4q^{19}+\cdots\)
5040.2.a.y 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.i \(0\) \(0\) \(1\) \(-1\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
5040.2.a.z 5040.a 1.a $1$ $40.245$ \(\Q\) None 630.2.a.c \(0\) \(0\) \(1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{13}-2q^{19}+q^{25}+\cdots\)
5040.2.a.ba 5040.a 1.a $1$ $40.245$ \(\Q\) None 210.2.a.d \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{13}+6q^{17}+4q^{19}+\cdots\)
5040.2.a.bb 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.h \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
5040.2.a.bc 5040.a 1.a $1$ $40.245$ \(\Q\) None 420.2.a.c \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+6q^{11}-4q^{13}-6q^{17}+\cdots\)
5040.2.a.bd 5040.a 1.a $1$ $40.245$ \(\Q\) None 140.2.a.b \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-5q^{11}-3q^{13}+q^{17}+\cdots\)
5040.2.a.be 5040.a 1.a $1$ $40.245$ \(\Q\) None 280.2.a.b \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-5q^{11}+q^{13}-3q^{17}+\cdots\)
5040.2.a.bf 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.g \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bg 5040.a 1.a $1$ $40.245$ \(\Q\) None 210.2.a.a \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bh 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.b \(0\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-4q^{11}+6q^{13}-4q^{17}+\cdots\)
5040.2.a.bi 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.c \(0\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
5040.2.a.bj 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.h \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+6q^{13}+2q^{17}-4q^{19}+\cdots\)
5040.2.a.bk 5040.a 1.a $1$ $40.245$ \(\Q\) None 2520.2.a.e \(0\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+2q^{11}-6q^{13}+2q^{17}+\cdots\)
5040.2.a.bl 5040.a 1.a $1$ $40.245$ \(\Q\) None 420.2.a.a \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+2q^{11}+4q^{13}-6q^{17}+\cdots\)
5040.2.a.bm 5040.a 1.a $1$ $40.245$ \(\Q\) None 70.2.a.a \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
5040.2.a.bn 5040.a 1.a $1$ $40.245$ \(\Q\) None 840.2.a.a \(0\) \(0\) \(1\) \(1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}-2q^{13}+6q^{17}+\cdots\)
5040.2.a.bo 5040.a 1.a $1$ $40.245$ \(\Q\) None 1260.2.a.b \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}-2q^{17}+6q^{19}+\cdots\)
5040.2.a.bp 5040.a 1.a $1$ $40.245$ \(\Q\) None 630.2.a.e \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+4q^{11}+6q^{13}+4q^{17}+\cdots\)
5040.2.a.bq 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None 280.2.a.d \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-\beta q^{11}+(2-3\beta )q^{13}+\cdots\)
5040.2.a.br 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{2}) \) None 840.2.a.k \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+\beta q^{11}+2q^{13}+(-2+\cdots)q^{17}+\cdots\)
5040.2.a.bs 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None 2520.2.a.u \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+(1+\beta )q^{11}+2q^{13}+(-1+\cdots)q^{17}+\cdots\)
5040.2.a.bt 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None 35.2.a.b \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+\beta q^{11}+(2+\beta )q^{13}+(2+\cdots)q^{17}+\cdots\)
5040.2.a.bu 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{2}) \) None 315.2.a.c \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}+(2+\beta )q^{11}+(-2+\beta )q^{13}+\cdots\)
5040.2.a.bv 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{17}) \) None 2520.2.a.u \(0\) \(0\) \(2\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+(-1-\beta )q^{11}+2q^{13}+\cdots\)
5040.2.a.bw 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{5}) \) None 105.2.a.b \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+(2+\beta )q^{11}+\beta q^{13}+2q^{17}+\cdots\)
5040.2.a.bx 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{2}) \) None 315.2.a.c \(0\) \(0\) \(2\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+(-2+\beta )q^{11}+(-2-\beta )q^{13}+\cdots\)
5040.2.a.by 5040.a 1.a $2$ $40.245$ \(\Q(\sqrt{33}) \) None 280.2.a.c \(0\) \(0\) \(2\) \(2\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+(4-\beta )q^{11}+(2-\beta )q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5040)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(420))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(560))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(840))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1260))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2520))\)\(^{\oplus 2}\)