Properties

Label 637.2.x
Level $637$
Weight $2$
Character orbit 637.x
Rep. character $\chi_{637}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $172$
Newform subspaces $3$
Sturm bound $130$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
Sturm bound: \(130\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 292 204 88
Cusp forms 228 172 56
Eisenstein series 64 32 32

Trace form

\( 172q + 2q^{2} + 6q^{4} + 6q^{5} - 12q^{6} - 20q^{8} - 140q^{9} + O(q^{10}) \) \( 172q + 2q^{2} + 6q^{4} + 6q^{5} - 12q^{6} - 20q^{8} - 140q^{9} + 12q^{10} - 10q^{11} - 8q^{12} - 46q^{15} + 66q^{16} + 6q^{17} - 36q^{18} + 8q^{19} + 36q^{20} - 4q^{22} + 6q^{23} - 12q^{24} - 24q^{26} - 4q^{29} + 38q^{31} + 44q^{32} - 18q^{33} - 12q^{34} - 138q^{36} - 12q^{37} - 96q^{39} - 48q^{40} - 18q^{41} - 26q^{44} - 12q^{45} - 26q^{46} + 42q^{47} - 12q^{48} - 90q^{50} + 120q^{51} + 28q^{52} - 8q^{53} + 30q^{54} + 6q^{55} + 16q^{57} - 62q^{58} + 6q^{59} + 108q^{60} + 36q^{62} - 6q^{65} - 66q^{66} + 60q^{67} - 30q^{68} - 42q^{69} + 10q^{71} + 94q^{72} - 14q^{73} + 74q^{74} + 20q^{75} - 52q^{76} + 22q^{78} - 20q^{79} - 12q^{80} - 28q^{81} + 108q^{82} + 66q^{83} + 102q^{85} + 14q^{86} - 42q^{87} + 30q^{89} + 72q^{90} + 188q^{92} + 118q^{93} - 18q^{95} - 18q^{96} - 62q^{97} + 48q^{99} + O(q^{100}) \)

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.x.a \(28\) \(5.086\) None \(-2\) \(0\) \(6\) \(0\)
637.2.x.b \(32\) \(5.086\) None \(4\) \(0\) \(0\) \(0\)
637.2.x.c \(112\) \(5.086\) None \(0\) \(0\) \(0\) \(0\)

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

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