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Properties

Label 2793.2.a
Level $2793$
Weight $2$
Character orbit 2793.a
Rep. character $\chi_{2793}(1,\cdot)$
Character field $\Q$
Dimension $122$
Newform subspaces $40$
Sturm bound $746$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2793.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 40 \)
Sturm bound: \(746\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2793))\).

Total New Old
Modular forms 388 122 266
Cusp forms 357 122 235
Eisenstein series 31 0 31

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

\(3\)\(7\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(14\)
\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(10\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(21\)
Plus space\(+\)\(54\)
Minus space\(-\)\(68\)

Trace form

\( 122 q + 2 q^{2} + 124 q^{4} - 6 q^{5} + 2 q^{6} + 6 q^{8} + 122 q^{9} + O(q^{10}) \) \( 122 q + 2 q^{2} + 124 q^{4} - 6 q^{5} + 2 q^{6} + 6 q^{8} + 122 q^{9} - 8 q^{10} + 6 q^{11} - 8 q^{12} - 12 q^{13} + 4 q^{15} + 136 q^{16} - 18 q^{17} + 2 q^{18} + 4 q^{19} + 4 q^{20} + 16 q^{22} + 12 q^{23} + 18 q^{24} + 116 q^{25} + 4 q^{26} + 8 q^{29} + 4 q^{30} - 4 q^{31} + 14 q^{32} + 8 q^{33} + 24 q^{34} + 124 q^{36} + 16 q^{37} - 16 q^{39} + 12 q^{40} - 12 q^{41} - 14 q^{43} + 56 q^{44} - 6 q^{45} + 52 q^{46} + 2 q^{47} - 14 q^{50} + 12 q^{51} + 24 q^{52} - 56 q^{53} + 2 q^{54} + 30 q^{55} - 2 q^{57} - 40 q^{58} + 16 q^{59} + 32 q^{60} - 14 q^{61} + 40 q^{62} + 176 q^{64} - 84 q^{65} - 12 q^{66} + 24 q^{67} - 12 q^{68} + 4 q^{69} + 48 q^{71} + 6 q^{72} - 18 q^{73} - 4 q^{74} - 8 q^{75} + 10 q^{76} + 20 q^{78} - 24 q^{79} + 88 q^{80} + 122 q^{81} + 56 q^{82} + 20 q^{83} - 54 q^{85} - 68 q^{86} + 20 q^{87} - 36 q^{88} - 40 q^{89} - 8 q^{90} - 52 q^{92} - 16 q^{93} + 24 q^{94} + 2 q^{95} + 58 q^{96} + 28 q^{97} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2793))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7 19
2793.2.a.a 2793.a 1.a $1$ $22.302$ \(\Q\) None 57.2.a.b \(-2\) \(-1\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{9}+\cdots\)
2793.2.a.b 2793.a 1.a $1$ $22.302$ \(\Q\) None 57.2.a.a \(-2\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+3q^{5}-2q^{6}+\cdots\)
2793.2.a.c 2793.a 1.a $1$ $22.302$ \(\Q\) None 399.2.a.b \(-1\) \(-1\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-4q^{5}+q^{6}+3q^{8}+\cdots\)
2793.2.a.d 2793.a 1.a $1$ $22.302$ \(\Q\) None 2793.2.a.d \(-1\) \(-1\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}+3q^{8}+\cdots\)
2793.2.a.e 2793.a 1.a $1$ $22.302$ \(\Q\) None 399.2.a.a \(-1\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
2793.2.a.f 2793.a 1.a $1$ $22.302$ \(\Q\) None 2793.2.a.d \(-1\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+2q^{5}-q^{6}+3q^{8}+\cdots\)
2793.2.a.g 2793.a 1.a $1$ $22.302$ \(\Q\) None 399.2.j.b \(0\) \(-1\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-2q^{5}+q^{9}-3q^{11}+\cdots\)
2793.2.a.h 2793.a 1.a $1$ $22.302$ \(\Q\) None 399.2.j.b \(0\) \(1\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+2q^{5}+q^{9}-3q^{11}+\cdots\)
2793.2.a.i 2793.a 1.a $1$ $22.302$ \(\Q\) None 57.2.a.c \(1\) \(-1\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-3q^{8}+\cdots\)
2793.2.a.j 2793.a 1.a $1$ $22.302$ \(\Q\) None 399.2.a.c \(1\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
2793.2.a.k 2793.a 1.a $1$ $22.302$ \(\Q\) None 399.2.j.a \(2\) \(-1\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}+q^{9}+\cdots\)
2793.2.a.l 2793.a 1.a $1$ $22.302$ \(\Q\) None 399.2.j.a \(2\) \(1\) \(1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}+q^{9}+\cdots\)
2793.2.a.m 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 2793.2.a.m \(-2\) \(-2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
2793.2.a.n 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 399.2.j.c \(-2\) \(-2\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{5}+\cdots\)
2793.2.a.o 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 399.2.j.c \(-2\) \(2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{5}+\cdots\)
2793.2.a.p 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 2793.2.a.m \(-2\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
2793.2.a.q 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{3}) \) None 2793.2.a.q \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}-\beta q^{8}+q^{9}+\cdots\)
2793.2.a.r 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{3}) \) None 2793.2.a.q \(0\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{8}+q^{9}+\cdots\)
2793.2.a.s 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 2793.2.a.s \(2\) \(-2\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}+2q^{5}-q^{6}-3q^{8}+\cdots\)
2793.2.a.t 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 2793.2.a.t \(2\) \(-2\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}-2\beta q^{5}+\cdots\)
2793.2.a.u 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 2793.2.a.s \(2\) \(2\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)
2793.2.a.v 2793.a 1.a $2$ $22.302$ \(\Q(\sqrt{2}) \) None 2793.2.a.t \(2\) \(2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(1+2\beta )q^{4}+2\beta q^{5}+\cdots\)
2793.2.a.w 2793.a 1.a $3$ $22.302$ 3.3.404.1 None 399.2.a.e \(1\) \(-3\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
2793.2.a.x 2793.a 1.a $3$ $22.302$ 3.3.148.1 None 399.2.a.d \(1\) \(3\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2793.2.a.y 2793.a 1.a $4$ $22.302$ 4.4.725.1 None 399.2.j.f \(-2\) \(-4\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(\beta _{2}-\beta _{3})q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
2793.2.a.z 2793.a 1.a $4$ $22.302$ 4.4.23301.1 None 399.2.j.e \(-2\) \(-4\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}-q^{3}+(2-\beta _{2})q^{4}+\cdots\)
2793.2.a.ba 2793.a 1.a $4$ $22.302$ 4.4.725.1 None 399.2.j.f \(-2\) \(4\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(\beta _{2}-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2793.2.a.bb 2793.a 1.a $4$ $22.302$ 4.4.23301.1 None 399.2.j.e \(-2\) \(4\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+q^{3}+(2-\beta _{2})q^{4}+\cdots\)
2793.2.a.bc 2793.a 1.a $4$ $22.302$ 4.4.1957.1 None 399.2.j.d \(0\) \(-4\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
2793.2.a.bd 2793.a 1.a $4$ $22.302$ 4.4.1957.1 None 399.2.j.d \(0\) \(4\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
2793.2.a.be 2793.a 1.a $5$ $22.302$ 5.5.1240016.1 None 399.2.a.f \(1\) \(-5\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}+(1+\beta _{4})q^{4}-\beta _{2}q^{5}+\cdots\)
2793.2.a.bf 2793.a 1.a $5$ $22.302$ 5.5.1244416.1 None 2793.2.a.bf \(3\) \(-5\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)
2793.2.a.bg 2793.a 1.a $5$ $22.302$ 5.5.368464.1 None 399.2.a.g \(3\) \(5\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2793.2.a.bh 2793.a 1.a $5$ $22.302$ 5.5.1244416.1 None 2793.2.a.bf \(3\) \(5\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}+\cdots\)
2793.2.a.bi 2793.a 1.a $6$ $22.302$ 6.6.5163008.1 None 2793.2.a.bi \(-2\) \(-6\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\cdots\)
2793.2.a.bj 2793.a 1.a $6$ $22.302$ 6.6.5163008.1 None 2793.2.a.bi \(-2\) \(6\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}-\beta _{3}+\beta _{4})q^{4}+\cdots\)
2793.2.a.bk 2793.a 1.a $6$ $22.302$ 6.6.39110656.1 None 2793.2.a.bk \(2\) \(-6\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-q^{3}+(2-\beta _{1}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2793.2.a.bl 2793.a 1.a $6$ $22.302$ 6.6.39110656.1 None 2793.2.a.bk \(2\) \(6\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}+(2-\beta _{1}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
2793.2.a.bm 2793.a 1.a $8$ $22.302$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 399.2.j.g \(0\) \(-8\) \(-5\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(-1-\beta _{5}+\cdots)q^{5}+\cdots\)
2793.2.a.bn 2793.a 1.a $8$ $22.302$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 399.2.j.g \(0\) \(8\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2793))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2793)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(399))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 2}\)