Properties

Label 637.2.g
Level $637$
Weight $2$
Character orbit 637.g
Rep. character $\chi_{637}(263,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $86$
Newform subspaces $13$
Sturm bound $130$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(130\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

Total New Old
Modular forms 146 102 44
Cusp forms 114 86 28
Eisenstein series 32 16 16

Trace form

\( 86q - q^{2} + 8q^{3} - 41q^{4} + 2q^{5} + 6q^{6} - 12q^{8} + 66q^{9} + O(q^{10}) \) \( 86q - q^{2} + 8q^{3} - 41q^{4} + 2q^{5} + 6q^{6} - 12q^{8} + 66q^{9} + 2q^{10} + 22q^{11} - 2q^{12} + 4q^{13} - 19q^{15} - 41q^{16} - 7q^{17} - 5q^{18} - 2q^{20} - 4q^{22} + 3q^{23} - 40q^{24} - 31q^{25} + 26q^{27} - 2q^{29} - 72q^{30} - 13q^{31} + 21q^{32} + 14q^{33} - 28q^{34} - 3q^{36} + q^{37} + 16q^{38} + 41q^{39} - 4q^{40} + 11q^{41} - 14q^{43} - 58q^{44} + 25q^{45} + 12q^{46} + 2q^{47} - 18q^{48} - 24q^{50} + 16q^{51} + 32q^{52} - 17q^{53} + 9q^{54} - 18q^{55} - 68q^{57} + 2q^{58} - 17q^{59} + 33q^{60} + 16q^{61} - 2q^{62} - 16q^{64} - 32q^{65} - 9q^{66} - 88q^{67} - 27q^{68} - 23q^{69} + q^{71} + 94q^{72} + 17q^{73} + 23q^{74} - 9q^{75} + 10q^{76} + 5q^{78} + 22q^{79} - 8q^{80} - 82q^{81} - 4q^{82} + 54q^{83} + 39q^{85} + 8q^{86} - 37q^{87} - 18q^{88} + 2q^{89} - 20q^{90} - 114q^{92} + 16q^{93} + 88q^{94} - 29q^{95} - 34q^{96} + 30q^{97} + 36q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
637.2.g.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(6\) \(3\) \(0\) \(q-\zeta_{6}q^{2}+3q^{3}+(1-\zeta_{6})q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
637.2.g.b \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(-6\) \(-3\) \(0\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+\cdots\)
637.2.g.c \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(6\) \(3\) \(0\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+\cdots\)
637.2.g.d \(4\) \(5.086\) \(\Q(\zeta_{12})\) None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(-1-\zeta_{12}^{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.g.e \(4\) \(5.086\) \(\Q(\zeta_{12})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}^{3})q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
637.2.g.f \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(-2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.g.g \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{3}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.g.h \(8\) \(5.086\) 8.0.\(\cdots\).7 None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+(-\beta _{5}+\beta _{6})q^{3}+\beta _{2}q^{4}+\cdots\)
637.2.g.i \(8\) \(5.086\) 8.0.\(\cdots\).6 None \(-2\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{5})q^{2}+\beta _{3}q^{3}+(-2-2\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.g.j \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-2\) \(-7\) \(0\) \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.g.k \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(2\) \(7\) \(0\) \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.g.l \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(2\) \(-1\) \(0\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+(-\beta _{3}+\beta _{11})q^{3}+\cdots\)
637.2.g.m \(16\) \(5.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{4}+\beta _{10})q^{2}+(\beta _{1}-\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(637, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(637, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)