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Properties

Label 304.4.bg
Level $304$
Weight $4$
Character orbit 304.bg
Rep. character $\chi_{304}(3,\cdot)$
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.bg (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

\( 1416 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8} + O(q^{10}) \) \( 1416 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 18 q^{8} - 174 q^{10} - 6 q^{11} - 18 q^{12} - 12 q^{13} + 36 q^{14} - 408 q^{16} - 24 q^{17} - 12 q^{19} - 24 q^{20} + 150 q^{21} - 12 q^{22} - 24 q^{23} - 12 q^{24} + 810 q^{26} - 18 q^{27} + 372 q^{28} - 12 q^{29} - 804 q^{30} + 498 q^{32} - 24 q^{33} - 1512 q^{34} + 738 q^{35} + 1284 q^{36} + 3426 q^{38} - 48 q^{39} - 1242 q^{40} - 756 q^{42} - 12 q^{43} - 2322 q^{44} - 6 q^{45} - 3168 q^{46} - 12 q^{48} - 31176 q^{49} + 6408 q^{50} + 2220 q^{51} + 1284 q^{52} - 12 q^{53} - 978 q^{54} - 24 q^{55} - 24 q^{58} - 12 q^{59} + 4566 q^{60} - 12 q^{61} + 36 q^{62} - 6 q^{64} - 36 q^{65} - 3312 q^{66} - 12 q^{67} + 1542 q^{68} - 4770 q^{69} + 534 q^{70} - 24 q^{71} + 9024 q^{72} - 5472 q^{74} + 2148 q^{76} + 4092 q^{77} - 324 q^{78} - 4752 q^{80} - 24 q^{81} + 4368 q^{82} - 6 q^{83} - 18 q^{84} - 1452 q^{85} - 12 q^{86} - 12 q^{87} - 18 q^{88} - 7032 q^{90} + 2046 q^{91} - 12 q^{92} + 150 q^{93} + 37884 q^{96} - 24 q^{97} - 888 q^{98} - 4386 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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