Properties

Label 912.2.br
Level $912$
Weight $2$
Character orbit 912.br
Rep. character $\chi_{912}(221,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $624$
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.br (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 912 \)
Character field: \(\Q(\zeta_{12})\)
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 656 656 0
Cusp forms 624 624 0
Eisenstein series 32 32 0

Trace form

\( 624q - 6q^{3} - 4q^{4} - 2q^{6} + O(q^{10}) \) \( 624q - 6q^{3} - 4q^{4} - 2q^{6} - 24q^{10} - 12q^{13} - 12q^{15} + 12q^{21} - 12q^{22} + 14q^{24} + 12q^{28} - 56q^{30} - 12q^{33} - 12q^{34} - 18q^{36} - 12q^{40} + 30q^{42} - 4q^{43} + 12q^{45} - 6q^{48} - 560q^{49} - 6q^{51} + 36q^{52} + 20q^{54} - 16q^{58} - 48q^{60} + 28q^{61} + 24q^{63} - 64q^{64} + 2q^{66} - 12q^{67} + 144q^{70} + 126q^{72} + 4q^{76} - 18q^{78} - 24q^{79} - 4q^{81} + 20q^{82} - 60q^{85} - 114q^{90} + 72q^{91} + 4q^{93} + 24q^{96} - 24q^{97} - 52q^{99} + O(q^{100}) \)

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.br.a \(624\) \(7.282\) None \(0\) \(-6\) \(0\) \(0\)