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Properties

Label 304.7.bh
Level $304$
Weight $7$
Character orbit 304.bh
Rep. character $\chi_{304}(35,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $2856$
Sturm bound $280$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 304.bh (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(304, [\chi])\).

Total New Old
Modular forms 2904 2904 0
Cusp forms 2856 2856 0
Eisenstein series 48 48 0

Trace form

\( 2856 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + O(q^{10}) \) \( 2856 q - 12 q^{2} - 12 q^{3} - 12 q^{4} - 12 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 3354 q^{10} - 6 q^{11} - 6 q^{12} - 12 q^{13} + 372 q^{14} + 2760 q^{16} - 24 q^{17} - 24 q^{18} - 12 q^{19} - 24 q^{20} + 4362 q^{21} - 12 q^{22} - 24 q^{23} - 12 q^{24} - 168918 q^{26} - 6 q^{27} + 24564 q^{28} - 12 q^{29} - 229032 q^{30} - 167802 q^{32} - 24 q^{33} - 418512 q^{34} + 93738 q^{35} + 384900 q^{36} - 24 q^{37} - 501366 q^{38} - 48 q^{39} - 431742 q^{40} + 1310124 q^{42} - 12 q^{43} - 852402 q^{44} - 6 q^{45} + 538644 q^{46} - 12 q^{48} - 22790304 q^{49} + 529068 q^{50} + 241044 q^{51} + 848868 q^{52} - 12 q^{53} + 1205802 q^{54} - 24 q^{55} + 1411764 q^{56} - 24 q^{58} - 12 q^{59} - 654666 q^{60} - 12 q^{61} - 396 q^{62} - 6 q^{64} - 12 q^{65} + 2795088 q^{66} - 12 q^{67} + 1385454 q^{68} - 1625190 q^{69} + 2409906 q^{70} - 24 q^{71} - 2855136 q^{72} - 3488952 q^{74} + 8286408 q^{75} - 2542332 q^{76} + 1411764 q^{77} - 298212 q^{78} + 1132848 q^{80} - 24 q^{81} + 3114168 q^{82} - 6 q^{83} + 1411782 q^{84} + 2231988 q^{85} - 12 q^{86} - 12 q^{87} - 6 q^{88} - 8599512 q^{90} + 705882 q^{91} - 12 q^{92} - 4386 q^{93} - 9408444 q^{94} + 5247060 q^{96} - 24 q^{97} + 5552016 q^{98} - 3188658 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

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