Properties

Label 637.2.w
Level $637$
Weight $2$
Character orbit 637.w
Rep. character $\chi_{637}(92,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $336$
Newform subspaces $2$
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.w (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 2 \)
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 396 336 60
Cusp forms 372 336 36
Eisenstein series 24 0 24

Trace form

\( 336q - 56q^{4} - 8q^{5} + 16q^{6} - 6q^{7} - 12q^{8} - 36q^{9} + O(q^{10}) \) \( 336q - 56q^{4} - 8q^{5} + 16q^{6} - 6q^{7} - 12q^{8} - 36q^{9} - 20q^{10} + 10q^{11} + 50q^{12} - 2q^{13} + 48q^{14} + 8q^{15} - 56q^{16} - 6q^{17} - 20q^{18} + 48q^{19} + 16q^{20} - 28q^{21} + 16q^{22} + 14q^{23} - 56q^{24} - 84q^{25} - 6q^{26} + 6q^{27} - 42q^{28} + 48q^{29} - 52q^{30} + 56q^{31} + 40q^{32} - 44q^{33} + 56q^{34} - 46q^{35} - 16q^{36} - 16q^{37} - 38q^{38} + 116q^{40} - 16q^{41} + 92q^{42} - 36q^{43} - 60q^{44} + 82q^{45} + 60q^{46} - 28q^{47} - 136q^{48} - 28q^{49} - 60q^{50} - 44q^{51} - 6q^{52} + 8q^{53} - 84q^{54} + 98q^{55} - 32q^{56} - 22q^{57} + 60q^{58} - 48q^{59} + 152q^{60} - 48q^{61} - 74q^{62} - 86q^{63} - 116q^{64} + 110q^{66} - 32q^{67} - 168q^{68} - 76q^{69} - 104q^{70} + 22q^{71} + 66q^{72} - 52q^{73} - 116q^{74} + 134q^{75} + 54q^{76} - 88q^{77} + 50q^{78} - 52q^{79} + 132q^{80} + 44q^{81} - 140q^{82} - 10q^{83} + 110q^{84} - 68q^{85} + 48q^{86} - 76q^{87} + 54q^{88} - 18q^{89} - 142q^{90} - 4q^{91} - 52q^{92} + 108q^{93} + 44q^{94} - 92q^{95} - 10q^{96} - 36q^{97} - 104q^{98} + 104q^{99} + O(q^{100}) \)

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.w.a \(162\) \(5.086\) None \(3\) \(0\) \(-4\) \(-15\)
637.2.w.b \(174\) \(5.086\) None \(-3\) \(0\) \(-4\) \(9\)

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

\( S_{2}^{\mathrm{old}}(637, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)