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Properties

Label 304.5.l
Level $304$
Weight $5$
Character orbit 304.l
Rep. character $\chi_{304}(115,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $200$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 304.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(200\)

Dimensions

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

Total New Old
Modular forms 324 288 36
Cusp forms 316 288 28
Eisenstein series 8 0 8

Trace form

\( 288 q + 12 q^{4} - 132 q^{6} + O(q^{10}) \) \( 288 q + 12 q^{4} - 132 q^{6} - 192 q^{11} + 660 q^{12} - 156 q^{14} - 620 q^{16} - 2720 q^{18} - 1200 q^{20} - 1804 q^{22} - 2304 q^{23} + 612 q^{24} + 2064 q^{26} + 3648 q^{27} + 3720 q^{28} - 1728 q^{29} + 5384 q^{30} - 3060 q^{32} - 6880 q^{34} - 15868 q^{36} + 3648 q^{37} - 5376 q^{39} + 10104 q^{40} + 17140 q^{42} - 3392 q^{43} + 10020 q^{44} - 620 q^{48} + 98784 q^{49} - 24696 q^{50} + 13760 q^{51} - 28268 q^{52} + 960 q^{53} - 5992 q^{54} + 23552 q^{55} + 12348 q^{56} + 31920 q^{58} + 5568 q^{59} + 27040 q^{60} + 38556 q^{62} - 8064 q^{64} + 4032 q^{65} - 39796 q^{66} - 18880 q^{67} - 26472 q^{68} - 1284 q^{70} - 39936 q^{71} + 43788 q^{72} + 18744 q^{74} - 2304 q^{75} + 9408 q^{77} + 48436 q^{78} - 7128 q^{80} - 209952 q^{81} + 14428 q^{82} + 10560 q^{83} - 48284 q^{84} + 37140 q^{86} - 64840 q^{88} - 13544 q^{90} + 46464 q^{91} + 36552 q^{92} - 17472 q^{93} + 5496 q^{94} + 6584 q^{96} + 5520 q^{98} - 49216 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{5}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)