Properties

Label 912.2.cp
Level $912$
Weight $2$
Character orbit 912.cp
Rep. character $\chi_{912}(35,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1872$
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.cp (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 912 \)
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 1968 0
Cusp forms 1872 1872 0
Eisenstein series 96 96 0

Trace form

\( 1872q - 12q^{3} - 24q^{4} - 12q^{6} - 24q^{7} + O(q^{10}) \) \( 1872q - 12q^{3} - 24q^{4} - 12q^{6} - 24q^{7} - 36q^{10} - 6q^{12} - 24q^{13} - 36q^{16} - 24q^{18} - 24q^{19} + 6q^{21} - 24q^{22} - 12q^{24} - 6q^{27} + 24q^{28} + 36q^{30} - 24q^{33} - 24q^{34} - 12q^{36} - 48q^{37} - 48q^{39} - 24q^{40} - 96q^{42} - 24q^{43} - 6q^{45} - 12q^{46} - 12q^{48} - 816q^{49} - 12q^{51} + 24q^{52} + 54q^{54} - 48q^{55} - 48q^{58} + 30q^{60} - 24q^{61} - 12q^{64} + 48q^{66} - 24q^{67} - 6q^{69} - 12q^{70} - 48q^{72} + 144q^{75} + 24q^{76} + 12q^{78} - 24q^{81} - 24q^{82} + 78q^{84} + 72q^{85} - 12q^{87} - 12q^{88} + 96q^{90} + 60q^{91} - 30q^{93} - 48q^{94} + 276q^{96} - 48q^{97} + 42q^{99} + O(q^{100}) \)

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.cp.a \(1872\) \(7.282\) None \(0\) \(-12\) \(0\) \(-24\)