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Properties

Label 931.2.a
Level $931$
Weight $2$
Character orbit 931.a
Rep. character $\chi_{931}(1,\cdot)$
Character field $\Q$
Dimension $62$
Newform subspaces $17$
Sturm bound $186$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(186\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(931))\).

Total New Old
Modular forms 100 62 38
Cusp forms 85 62 23
Eisenstein series 15 0 15

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

\(7\)\(19\)FrickeDim
\(+\)\(+\)$+$\(14\)
\(+\)\(-\)$-$\(18\)
\(-\)\(+\)$-$\(18\)
\(-\)\(-\)$+$\(12\)
Plus space\(+\)\(26\)
Minus space\(-\)\(36\)

Trace form

\( 62 q - q^{2} + 2 q^{3} + 61 q^{4} + 3 q^{5} + 3 q^{8} + 58 q^{9} + O(q^{10}) \) \( 62 q - q^{2} + 2 q^{3} + 61 q^{4} + 3 q^{5} + 3 q^{8} + 58 q^{9} + 10 q^{10} - 3 q^{11} + 12 q^{12} + 10 q^{13} + 2 q^{15} + 51 q^{16} + 5 q^{17} - 17 q^{18} - 2 q^{19} - 20 q^{22} - 4 q^{23} - 20 q^{24} + 69 q^{25} - 2 q^{26} + 8 q^{27} - 20 q^{29} - 32 q^{30} + 12 q^{31} - 25 q^{32} - 30 q^{33} - 18 q^{34} + 33 q^{36} + 12 q^{37} - 3 q^{38} - 8 q^{39} - 6 q^{40} - 4 q^{41} + 9 q^{43} - 26 q^{44} + 15 q^{45} - 56 q^{46} - 9 q^{47} + 44 q^{48} + 13 q^{50} - 70 q^{51} + 6 q^{52} + 30 q^{53} - 16 q^{54} - 21 q^{55} + 2 q^{57} + 10 q^{58} + 6 q^{59} - 12 q^{60} + 7 q^{61} - 4 q^{62} + 39 q^{64} + 24 q^{65} + 24 q^{66} - 32 q^{67} + 36 q^{68} - 28 q^{69} - 46 q^{71} + 7 q^{72} + 13 q^{73} - 22 q^{74} + 12 q^{75} - 5 q^{76} - 12 q^{78} - 24 q^{79} - 38 q^{80} + 10 q^{81} - 18 q^{82} - 32 q^{83} + 37 q^{85} + 20 q^{86} - 40 q^{87} + 2 q^{89} + 102 q^{90} + 60 q^{92} + 16 q^{93} + 12 q^{94} + 7 q^{95} - 16 q^{96} + 2 q^{97} - 3 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(931))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 7 19
931.2.a.a 931.a 1.a $1$ $7.434$ \(\Q\) None \(0\) \(2\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-3q^{5}+q^{9}+3q^{11}+\cdots\)
931.2.a.b 931.a 1.a $1$ $7.434$ \(\Q\) None \(2\) \(-2\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}-3q^{5}-4q^{6}+\cdots\)
931.2.a.c 931.a 1.a $1$ $7.434$ \(\Q\) None \(2\) \(2\) \(3\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}+3q^{5}+4q^{6}+\cdots\)
931.2.a.d 931.a 1.a $2$ $7.434$ \(\Q(\sqrt{5}) \) None \(-3\) \(3\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots\)
931.2.a.e 931.a 1.a $2$ $7.434$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
931.2.a.f 931.a 1.a $2$ $7.434$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
931.2.a.g 931.a 1.a $2$ $7.434$ \(\Q(\sqrt{13}) \) None \(-1\) \(3\) \(6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2-\beta )q^{3}+(1+\beta )q^{4}+3q^{5}+\cdots\)
931.2.a.h 931.a 1.a $2$ $7.434$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+2\beta q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
931.2.a.i 931.a 1.a $2$ $7.434$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}-2\beta q^{5}+2q^{6}-2\beta q^{8}+\cdots\)
931.2.a.j 931.a 1.a $2$ $7.434$ \(\Q(\sqrt{5}) \) None \(1\) \(-3\) \(-2\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
931.2.a.k 931.a 1.a $3$ $7.434$ 3.3.229.1 None \(2\) \(-3\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
931.2.a.l 931.a 1.a $4$ $7.434$ 4.4.5744.1 None \(0\) \(-2\) \(-8\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
931.2.a.m 931.a 1.a $4$ $7.434$ 4.4.5744.1 None \(0\) \(2\) \(8\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
931.2.a.n 931.a 1.a $7$ $7.434$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(-2\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(1+\beta _{3}-\beta _{5})q^{4}+\cdots\)
931.2.a.o 931.a 1.a $7$ $7.434$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(1+\beta _{3}-\beta _{5})q^{4}+\cdots\)
931.2.a.p 931.a 1.a $10$ $7.434$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-4\) \(-16\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
931.2.a.q 931.a 1.a $10$ $7.434$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(4\) \(16\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(2+\beta _{9})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(931))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(931)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 2}\)