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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 7 19
931.2.a.a \(1\) \(7.434\) \(\Q\) None \(0\) \(2\) \(-3\) \(0\) \(-\) \(+\) \(q+2q^{3}-2q^{4}-3q^{5}+q^{9}+3q^{11}+\cdots\)
931.2.a.b \(1\) \(7.434\) \(\Q\) None \(2\) \(-2\) \(-3\) \(0\) \(-\) \(+\) \(q+2q^{2}-2q^{3}+2q^{4}-3q^{5}-4q^{6}+\cdots\)
931.2.a.c \(1\) \(7.434\) \(\Q\) None \(2\) \(2\) \(3\) \(0\) \(+\) \(-\) \(q+2q^{2}+2q^{3}+2q^{4}+3q^{5}+4q^{6}+\cdots\)
931.2.a.d \(2\) \(7.434\) \(\Q(\sqrt{5}) \) None \(-3\) \(3\) \(0\) \(0\) \(-\) \(-\) \(q+(-1-\beta )q^{2}+(1+\beta )q^{3}+3\beta q^{4}+\cdots\)
931.2.a.e \(2\) \(7.434\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-2\) \(0\) \(-\) \(-\) \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
931.2.a.f \(2\) \(7.434\) \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(0\) \(+\) \(+\) \(q+(-1+\beta )q^{2}-\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
931.2.a.g \(2\) \(7.434\) \(\Q(\sqrt{13}) \) None \(-1\) \(3\) \(6\) \(0\) \(-\) \(+\) \(q-\beta q^{2}+(2-\beta )q^{3}+(1+\beta )q^{4}+3q^{5}+\cdots\)
931.2.a.h \(2\) \(7.434\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(-\) \(-\) \(q+\beta q^{2}-\beta q^{3}+2\beta q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
931.2.a.i \(2\) \(7.434\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) \(+\) \(+\) \(q+\beta q^{2}+\beta q^{3}-2\beta q^{5}+2q^{6}-2\beta q^{8}+\cdots\)
931.2.a.j \(2\) \(7.434\) \(\Q(\sqrt{5}) \) None \(1\) \(-3\) \(-2\) \(0\) \(-\) \(-\) \(q+\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
931.2.a.k \(3\) \(7.434\) 3.3.229.1 None \(2\) \(-3\) \(2\) \(0\) \(-\) \(+\) \(q+(1+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
931.2.a.l \(4\) \(7.434\) 4.4.5744.1 None \(0\) \(-2\) \(-8\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
931.2.a.m \(4\) \(7.434\) 4.4.5744.1 None \(0\) \(2\) \(8\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
931.2.a.n \(7\) \(7.434\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(-2\) \(-2\) \(0\) \(+\) \(-\) \(q+\beta _{3}q^{2}-\beta _{2}q^{3}+(1+\beta _{3}-\beta _{5})q^{4}+\cdots\)
931.2.a.o \(7\) \(7.434\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(2\) \(2\) \(0\) \(-\) \(+\) \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(1+\beta _{3}-\beta _{5})q^{4}+\cdots\)
931.2.a.p \(10\) \(7.434\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(-4\) \(-16\) \(0\) \(+\) \(+\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
931.2.a.q \(10\) \(7.434\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(4\) \(16\) \(0\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(2+\beta _{9})q^{5}+\cdots\)

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

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