Properties

Label 304.2.bi
Level $304$
Weight $2$
Character orbit 304.bi
Rep. character $\chi_{304}(5,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $456$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.bi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

Total New Old
Modular forms 504 504 0
Cusp forms 456 456 0
Eisenstein series 48 48 0

Trace form

\( 456q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 6q^{8} + O(q^{10}) \) \( 456q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 6q^{8} - 18q^{10} - 6q^{11} - 6q^{12} - 12q^{13} - 24q^{14} - 24q^{15} - 24q^{16} - 24q^{17} - 24q^{18} - 12q^{19} - 24q^{20} - 30q^{21} - 12q^{22} - 12q^{24} - 54q^{26} - 6q^{27} - 36q^{28} - 12q^{29} + 36q^{30} + 60q^{31} - 42q^{32} - 24q^{33} - 72q^{34} - 42q^{35} - 60q^{36} - 24q^{37} + 102q^{38} + 18q^{40} - 168q^{42} - 12q^{43} + 54q^{44} - 6q^{45} + 24q^{46} - 24q^{47} - 12q^{48} + 144q^{49} - 24q^{50} + 12q^{51} + 36q^{52} - 12q^{53} + 102q^{54} - 108q^{56} - 24q^{58} - 12q^{59} + 30q^{60} - 12q^{61} - 108q^{63} - 6q^{64} - 12q^{65} - 72q^{66} - 12q^{67} + 30q^{68} - 54q^{69} + 18q^{70} - 144q^{72} - 96q^{74} - 192q^{75} - 60q^{76} - 108q^{77} - 60q^{78} - 24q^{79} + 48q^{80} - 24q^{81} + 48q^{82} - 6q^{83} - 90q^{84} + 84q^{85} - 12q^{86} - 6q^{88} + 96q^{90} - 54q^{91} - 12q^{92} + 6q^{93} + 60q^{94} - 24q^{95} + 84q^{96} - 24q^{97} - 66q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
304.2.bi.a \(456\) \(2.427\) None \(-12\) \(-12\) \(-12\) \(0\)