Properties

Label 304.2.bg
Level $304$
Weight $2$
Character orbit 304.bg
Rep. character $\chi_{304}(3,\cdot)$
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.bg (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

\( 456q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 12q^{7} - 18q^{8} + O(q^{10}) \) \( 456q - 12q^{2} - 12q^{3} - 12q^{4} - 12q^{5} - 12q^{6} - 12q^{7} - 18q^{8} - 42q^{10} - 6q^{11} - 18q^{12} - 12q^{13} - 24q^{16} - 24q^{17} - 12q^{19} - 24q^{20} + 6q^{21} - 12q^{22} - 24q^{23} - 12q^{24} - 54q^{26} - 18q^{27} + 12q^{28} - 12q^{29} - 48q^{30} + 18q^{32} - 24q^{33} + 48q^{34} + 18q^{35} - 60q^{36} - 66q^{38} - 48q^{39} - 42q^{40} + 144q^{42} - 12q^{43} + 54q^{44} - 6q^{45} - 108q^{46} - 12q^{48} - 168q^{49} + 36q^{50} + 12q^{51} - 60q^{52} - 12q^{53} - 126q^{54} - 24q^{55} - 24q^{58} - 12q^{59} + 30q^{60} - 12q^{61} - 6q^{64} - 36q^{65} - 72q^{66} - 12q^{67} - 42q^{68} + 126q^{69} + 102q^{70} - 24q^{71} - 48q^{72} + 72q^{74} + 36q^{76} + 60q^{77} - 108q^{78} + 48q^{80} - 24q^{81} - 72q^{82} - 6q^{83} - 18q^{84} - 108q^{85} - 12q^{86} - 12q^{87} - 18q^{88} + 96q^{90} + 30q^{91} - 12q^{92} + 6q^{93} - 132q^{96} - 24q^{97} - 66q^{99} + O(q^{100}) \)

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.bg.a \(456\) \(2.427\) None \(-12\) \(-12\) \(-12\) \(-12\)