Properties

Label 912.2.cq
Level $912$
Weight $2$
Character orbit 912.cq
Rep. character $\chi_{912}(61,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $960$
Newform subspaces $1$
Sturm bound $320$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cq (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(320\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(912, [\chi])\).

Total New Old
Modular forms 1968 960 1008
Cusp forms 1872 960 912
Eisenstein series 96 0 96

Trace form

\( 960q + O(q^{10}) \) \( 960q + 24q^{10} + 12q^{16} - 144q^{31} + 60q^{32} + 120q^{34} + 12q^{36} - 228q^{38} - 60q^{40} - 60q^{46} + 480q^{49} + 36q^{50} - 24q^{51} - 48q^{52} - 12q^{54} - 72q^{68} + 48q^{69} - 72q^{70} + 48q^{76} + 72q^{78} - 120q^{80} - 120q^{82} - 96q^{85} - 168q^{94} - 84q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(912, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
912.2.cq.a \(960\) \(7.282\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(912, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(912, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(304, [\chi])\)\(^{\oplus 2}\)