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Properties

Label 304.4.v
Level $304$
Weight $4$
Character orbit 304.v
Rep. character $\chi_{304}(45,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $472$
Sturm bound $160$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 76 q^{8} + O(q^{10}) \) \( 472 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 76 q^{8} - 68 q^{10} - 8 q^{11} - 8 q^{12} - 2 q^{13} + 14 q^{14} + 236 q^{15} + 130 q^{16} - 4 q^{17} - 40 q^{18} + 20 q^{19} + 300 q^{20} + 52 q^{21} - 2 q^{22} + 822 q^{24} - 572 q^{26} - 116 q^{27} - 254 q^{28} - 2 q^{29} + 1088 q^{30} + 1472 q^{31} - 452 q^{32} - 4 q^{33} - 416 q^{34} - 208 q^{35} - 690 q^{36} - 8 q^{37} - 658 q^{38} - 412 q^{40} + 770 q^{42} - 2 q^{43} + 1300 q^{44} - 400 q^{45} - 176 q^{46} - 4 q^{47} - 42 q^{48} - 20792 q^{49} - 4316 q^{50} - 638 q^{51} + 430 q^{52} - 2 q^{53} - 1188 q^{54} + 5276 q^{56} + 1364 q^{58} - 2 q^{59} - 3720 q^{60} - 1826 q^{61} - 1586 q^{62} + 1368 q^{63} - 1100 q^{64} - 16 q^{65} + 42 q^{66} - 1850 q^{67} + 744 q^{68} + 1996 q^{69} + 5328 q^{70} - 966 q^{72} - 3722 q^{74} - 6224 q^{75} + 3382 q^{76} + 2736 q^{77} + 86 q^{78} + 8820 q^{79} + 6406 q^{80} + 16520 q^{81} + 3706 q^{82} + 2672 q^{83} - 1004 q^{84} + 738 q^{85} - 1186 q^{86} - 4308 q^{88} + 286 q^{90} + 684 q^{91} - 606 q^{92} - 56 q^{93} - 11360 q^{94} - 3872 q^{95} + 10720 q^{96} - 4 q^{97} - 3222 q^{98} - 1092 q^{99} + O(q^{100}) \)

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.