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Properties

Label 1116.2.a
Level $1116$
Weight $2$
Character orbit 1116.a
Rep. character $\chi_{1116}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $9$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1116.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1116))\).

Total New Old
Modular forms 204 12 192
Cusp forms 181 12 169
Eisenstein series 23 0 23

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

\(2\)\(3\)\(31\)FrickeDim
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(4\)
Plus space\(+\)\(6\)
Minus space\(-\)\(6\)

Trace form

\( 12 q + 2 q^{5} + 2 q^{7} - 4 q^{11} - 6 q^{13} - 2 q^{17} - 14 q^{19} + 6 q^{23} + 6 q^{25} - 10 q^{29} - 18 q^{35} + 8 q^{37} + 2 q^{41} - 6 q^{43} + 16 q^{47} - 2 q^{49} - 8 q^{53} - 8 q^{55} + 18 q^{59}+ \cdots - 10 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1116))\) 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 31
1116.2.a.a 1116.a 1.a $1$ $8.911$ \(\Q\) None 372.2.a.d \(0\) \(0\) \(-3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}+2q^{13}-q^{19}+6q^{23}+\cdots\)
1116.2.a.b 1116.a 1.a $1$ $8.911$ \(\Q\) None 124.2.a.b \(0\) \(0\) \(-1\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-6q^{11}-4q^{13}-5q^{19}+\cdots\)
1116.2.a.c 1116.a 1.a $1$ $8.911$ \(\Q\) None 372.2.a.a \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-6q^{13}+8q^{17}+7q^{19}+\cdots\)
1116.2.a.d 1116.a 1.a $1$ $8.911$ \(\Q\) None 372.2.a.c \(0\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}+2q^{13}+4q^{19}-4q^{23}+\cdots\)
1116.2.a.e 1116.a 1.a $1$ $8.911$ \(\Q\) None 372.2.a.b \(0\) \(0\) \(3\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-5q^{7}-2q^{11}-4q^{13}+4q^{17}+\cdots\)
1116.2.a.f 1116.a 1.a $1$ $8.911$ \(\Q\) None 124.2.a.a \(0\) \(0\) \(3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-q^{7}+6q^{11}+2q^{13}-6q^{17}+\cdots\)
1116.2.a.g 1116.a 1.a $2$ $8.911$ \(\Q(\sqrt{17}) \) None 372.2.a.e \(0\) \(0\) \(-3\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-1+\beta )q^{7}+(-2+\cdots)q^{11}+\cdots\)
1116.2.a.h 1116.a 1.a $2$ $8.911$ \(\Q(\sqrt{3}) \) None 1116.2.a.h \(0\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}-2\beta q^{11}-4q^{13}-4\beta q^{17}+\cdots\)
1116.2.a.i 1116.a 1.a $2$ $8.911$ \(\Q(\sqrt{7}) \) None 1116.2.a.i \(0\) \(0\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+3q^{7}+2q^{13}+q^{19}+2\beta q^{23}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1116))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1116)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(279))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(372))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(558))\)\(^{\oplus 2}\)