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Properties

Label 1815.4.c
Level $1815$
Weight $4$
Character orbit 1815.c
Rep. character $\chi_{1815}(364,\cdot)$
Character field $\Q$
Dimension $328$
Sturm bound $1056$

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Defining parameters

Level: \( N \) \(=\) \( 1815 = 3 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1815.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1815, [\chi])\).

Total New Old
Modular forms 816 328 488
Cusp forms 768 328 440
Eisenstein series 48 0 48

Trace form

\( 328 q - 1314 q^{4} + 22 q^{5} - 6 q^{6} - 2952 q^{9} + O(q^{10}) \) \( 328 q - 1314 q^{4} + 22 q^{5} - 6 q^{6} - 2952 q^{9} + 62 q^{10} + 36 q^{14} - 54 q^{15} + 5490 q^{16} + 280 q^{19} - 272 q^{20} - 132 q^{21} - 18 q^{24} - 52 q^{25} - 724 q^{26} + 636 q^{29} - 60 q^{30} + 872 q^{31} - 108 q^{34} + 228 q^{35} + 11826 q^{36} + 132 q^{39} - 2206 q^{40} - 312 q^{41} - 198 q^{45} + 1160 q^{46} - 17744 q^{49} - 1600 q^{50} + 132 q^{51} + 54 q^{54} + 60 q^{56} + 908 q^{59} + 294 q^{60} + 48 q^{61} - 20650 q^{64} + 2284 q^{65} - 864 q^{69} - 2204 q^{70} - 392 q^{71} + 4892 q^{74} + 1104 q^{75} + 256 q^{76} + 3504 q^{79} + 4252 q^{80} + 26568 q^{81} + 3996 q^{84} - 932 q^{85} - 5832 q^{86} - 832 q^{89} - 558 q^{90} + 1960 q^{91} + 400 q^{94} - 3576 q^{95} - 4542 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1815, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1815, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \cong \)