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Properties

Label 1815.4.bm
Level $1815$
Weight $4$
Character orbit 1815.bm
Rep. character $\chi_{1815}(4,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $15840$
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.bm (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 31840 15840 16000
Cusp forms 31520 15840 15680
Eisenstein series 320 0 320

Trace form

\( 15840 q - 1584 q^{4} - 16 q^{5} + 24 q^{6} + 35640 q^{9} + O(q^{10}) \) \( 15840 q - 1584 q^{4} - 16 q^{5} + 24 q^{6} + 35640 q^{9} - 180 q^{10} + 532 q^{11} + 24 q^{14} - 102 q^{15} + 6552 q^{16} - 392 q^{19} + 826 q^{20} - 672 q^{21} - 288 q^{24} + 728 q^{25} + 244 q^{26} - 564 q^{30} + 612 q^{31} + 144 q^{34} + 632 q^{35} + 14256 q^{36} - 600 q^{39} + 1174 q^{40} + 1716 q^{41} - 7908 q^{44} + 144 q^{45} + 3104 q^{46} - 20088 q^{49} - 5770 q^{50} + 1320 q^{51} + 864 q^{54} + 7208 q^{55} + 1704 q^{56} + 128 q^{59} - 432 q^{60} + 4152 q^{61} - 30156 q^{64} - 5752 q^{65} - 3204 q^{66} - 1968 q^{69} - 1720 q^{70} + 1968 q^{71} - 8024 q^{74} + 1704 q^{75} + 5900 q^{76} - 76 q^{79} + 2342 q^{80} - 320760 q^{81} - 1944 q^{84} - 3084 q^{85} + 3680 q^{86} - 1400 q^{89} + 1956 q^{91} + 5812 q^{94} - 3440 q^{95} + 2688 q^{96} - 4788 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)