Properties

Label 637.2.f
Level $637$
Weight $2$
Character orbit 637.f
Rep. character $\chi_{637}(295,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $84$
Newform subspaces $12$
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.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
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 148 104 44
Cusp forms 116 84 32
Eisenstein series 32 20 12

Trace form

\( 84q + 2q^{2} - 34q^{4} + 8q^{5} - 6q^{6} - 24q^{8} - 26q^{9} + O(q^{10}) \) \( 84q + 2q^{2} - 34q^{4} + 8q^{5} - 6q^{6} - 24q^{8} - 26q^{9} + 2q^{10} - 2q^{11} - 4q^{12} + 2q^{13} - 10q^{15} - 10q^{16} - 10q^{17} - 20q^{18} + 8q^{19} + 10q^{20} - 4q^{22} + 6q^{23} - 28q^{24} + 60q^{25} + 12q^{26} + 36q^{27} - 8q^{29} + 24q^{30} + 4q^{31} + 6q^{32} - 22q^{33} + 8q^{34} - 26q^{36} - 30q^{37} + 52q^{38} - 12q^{39} + 8q^{40} - 16q^{41} + 56q^{44} + 10q^{45} + 48q^{46} - 28q^{47} - 26q^{48} + 24q^{50} + 40q^{51} - 78q^{52} + 28q^{53} - 6q^{55} - 10q^{58} + 10q^{59} - 12q^{60} - 24q^{61} + 4q^{62} - 72q^{64} - 56q^{65} - 12q^{66} + 16q^{67} - 66q^{68} + 4q^{69} - 14q^{71} + 22q^{72} + 16q^{73} + 50q^{74} - 14q^{75} + 18q^{76} + 110q^{78} - 72q^{79} + 34q^{80} + 54q^{81} - 28q^{82} - 12q^{83} + 42q^{85} - 64q^{86} - 10q^{87} + 30q^{88} + 32q^{89} - 116q^{90} - 36q^{92} + 36q^{93} + 52q^{94} - 14q^{95} + 212q^{96} + 26q^{97} - 96q^{99} + O(q^{100}) \)

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.f.a \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-6\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.f.b \(2\) \(5.086\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(6\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(3-3\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
637.2.f.c \(4\) \(5.086\) \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-3\) \(-3\) \(-6\) \(0\) \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+\cdots\)
637.2.f.d \(4\) \(5.086\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{2}+(\zeta_{12}+\zeta_{12}^{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
637.2.f.e \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(-4\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}-\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.f \(4\) \(5.086\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(4\) \(0\) \(q+(1+\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.g \(8\) \(5.086\) 8.0.\(\cdots\).7 None \(-4\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
637.2.f.h \(8\) \(5.086\) 8.0.\(\cdots\).6 None \(-2\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2}-\beta _{6})q^{2}+(-\beta _{3}+\beta _{7})q^{3}+\cdots\)
637.2.f.i \(8\) \(5.086\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(1\) \(14\) \(0\) \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
637.2.f.j \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-1\) \(2\) \(0\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{11}q^{3}+\cdots\)
637.2.f.k \(12\) \(5.086\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(1\) \(-2\) \(0\) \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}+\beta _{11}q^{3}+\cdots\)
637.2.f.l \(16\) \(5.086\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{4}+\beta _{10})q^{2}+(\beta _{8}-\beta _{15})q^{3}+\cdots\)

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

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