Properties

Label 1815.4.s
Level $1815$
Weight $4$
Character orbit 1815.s
Rep. character $\chi_{1815}(124,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $1296$
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.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 3264 1296 1968
Cusp forms 3072 1296 1776
Eisenstein series 192 0 192

Trace form

\( 1296 q + 1296 q^{4} - 16 q^{5} + 24 q^{6} + 2916 q^{9} + O(q^{10}) \) \( 1296 q + 1296 q^{4} - 16 q^{5} + 24 q^{6} + 2916 q^{9} - 48 q^{10} + 232 q^{14} - 102 q^{15} - 5080 q^{16} - 392 q^{19} + 826 q^{20} - 672 q^{21} - 288 q^{24} + 728 q^{25} + 612 q^{26} - 564 q^{30} + 612 q^{31} + 3152 q^{34} + 632 q^{35} - 11664 q^{36} - 600 q^{39} + 1174 q^{40} + 1716 q^{41} + 144 q^{45} + 3104 q^{46} + 17304 q^{49} + 2194 q^{50} + 1320 q^{51} + 864 q^{54} - 720 q^{56} + 1504 q^{59} + 792 q^{60} + 4152 q^{61} + 14948 q^{64} - 4696 q^{65} - 1968 q^{69} + 3464 q^{70} - 3360 q^{71} - 8024 q^{74} + 1080 q^{75} - 17904 q^{76} - 1924 q^{79} - 818 q^{80} - 26244 q^{81} - 1944 q^{84} - 3436 q^{85} + 11808 q^{86} - 1400 q^{89} - 1188 q^{90} + 3364 q^{91} - 17068 q^{94} - 3440 q^{95} + 2688 q^{96} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1815, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)