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Properties

Label 1815.4.f
Level $1815$
Weight $4$
Character orbit 1815.f
Rep. character $\chi_{1815}(1451,\cdot)$
Character field $\Q$
Dimension $432$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 816 432 384
Cusp forms 768 432 336
Eisenstein series 48 0 48

Trace form

\( 432 q + 4 q^{3} + 1728 q^{4} + 28 q^{9} + O(q^{10}) \) \( 432 q + 4 q^{3} + 1728 q^{4} + 28 q^{9} + 48 q^{12} + 40 q^{15} + 6432 q^{16} - 10800 q^{25} + 628 q^{27} + 24 q^{31} + 1704 q^{34} - 1144 q^{36} + 432 q^{37} - 2052 q^{42} - 604 q^{48} - 21792 q^{49} + 5376 q^{58} + 1620 q^{60} + 22800 q^{64} + 168 q^{67} - 3872 q^{69} + 1080 q^{70} - 100 q^{75} - 4052 q^{78} - 9204 q^{81} - 8808 q^{82} - 4224 q^{91} + 3120 q^{93} + 4776 q^{97} + O(q^{100}) \)

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

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