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Properties

Label 304.5.bh
Level $304$
Weight $5$
Character orbit 304.bh
Rep. character $\chi_{304}(35,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $1896$
Sturm bound $200$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 304.bh (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(304, [\chi])\).

Total New Old
Modular forms 1944 1944 0
Cusp forms 1896 1896 0
Eisenstein series 48 48 0

Trace form

\( 1896 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + O(q^{10}) \) \( 1896 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 282 q^{10} - 6 q^{11} - 6 q^{12} - 12 q^{13} + 84 q^{14} + 1416 q^{16} - 24 q^{17} - 24 q^{18} - 12 q^{19} - 24 q^{20} + 474 q^{21} - 12 q^{22} - 24 q^{23} - 12 q^{24} + 6186 q^{26} - 6 q^{27} + 1524 q^{28} - 12 q^{29} - 3240 q^{30} - 3162 q^{32} - 24 q^{33} + 10608 q^{34} + 3738 q^{35} - 9084 q^{36} - 24 q^{37} + 618 q^{38} - 48 q^{39} + 258 q^{40} - 27636 q^{42} - 12 q^{43} + 15630 q^{44} - 6 q^{45} + 2964 q^{46} - 12 q^{48} - 300480 q^{49} + 16140 q^{50} - 12108 q^{51} - 18972 q^{52} - 12 q^{53} - 15606 q^{54} - 24 q^{55} + 28788 q^{56} - 24 q^{58} - 12 q^{59} + 26742 q^{60} - 12 q^{61} - 108 q^{62} - 6 q^{64} - 12 q^{65} + 7248 q^{66} - 12 q^{67} - 19986 q^{68} + 29370 q^{69} - 31470 q^{70} - 24 q^{71} - 12576 q^{72} + 35016 q^{74} - 90072 q^{75} - 16380 q^{76} + 28788 q^{77} - 48804 q^{78} - 9552 q^{80} - 24 q^{81} - 27912 q^{82} - 6 q^{83} + 28806 q^{84} + 67188 q^{85} - 12 q^{86} - 12 q^{87} - 6 q^{88} + 83688 q^{90} + 14394 q^{91} - 12 q^{92} - 498 q^{93} + 46596 q^{94} - 197292 q^{96} - 24 q^{97} + 29232 q^{98} - 39378 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

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