Properties

Label 304.4.bi
Level $304$
Weight $4$
Character orbit 304.bi
Rep. character $\chi_{304}(5,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1416$
Sturm bound $160$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 304.bi (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(304, [\chi])\).

Total New Old
Modular forms 1464 1464 0
Cusp forms 1416 1416 0
Eisenstein series 48 48 0

Trace form

\( 1416 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} + O(q^{10}) \) \( 1416 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 6 q^{8} + 186 q^{10} - 6 q^{11} - 6 q^{12} - 12 q^{13} - 60 q^{14} - 24 q^{15} - 408 q^{16} - 24 q^{17} - 24 q^{18} - 12 q^{19} - 24 q^{20} - 174 q^{21} - 12 q^{22} - 12 q^{24} + 810 q^{26} - 6 q^{27} - 396 q^{28} - 12 q^{29} + 792 q^{30} - 2244 q^{31} - 522 q^{32} - 24 q^{33} + 1488 q^{34} - 762 q^{35} + 1284 q^{36} - 24 q^{37} - 2790 q^{38} + 1218 q^{40} + 732 q^{42} - 12 q^{43} - 2322 q^{44} - 6 q^{45} + 1044 q^{46} - 24 q^{47} - 12 q^{48} + 31152 q^{49} - 2148 q^{50} + 2220 q^{51} - 1308 q^{52} - 12 q^{53} + 954 q^{54} - 4140 q^{56} - 24 q^{58} - 12 q^{59} + 4566 q^{60} - 12 q^{61} + 36 q^{62} - 4140 q^{63} - 6 q^{64} - 12 q^{65} - 3312 q^{66} - 12 q^{67} - 1554 q^{68} + 1578 q^{69} - 3582 q^{70} + 2880 q^{72} + 5448 q^{74} + 9888 q^{75} - 2172 q^{76} - 4140 q^{77} - 132 q^{78} - 24 q^{79} - 4752 q^{80} - 24 q^{81} - 4392 q^{82} - 6 q^{83} - 4122 q^{84} + 1428 q^{85} - 12 q^{86} - 6 q^{88} - 7032 q^{90} - 2070 q^{91} - 12 q^{92} + 150 q^{93} + 10980 q^{94} - 24 q^{95} - 37932 q^{96} - 24 q^{97} + 960 q^{98} - 4386 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.