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Properties

Label 735.4.p
Level $735$
Weight $4$
Character orbit 735.p
Rep. character $\chi_{735}(374,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $464$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 735.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(735, [\chi])\).

Total New Old
Modular forms 704 496 208
Cusp forms 640 464 176
Eisenstein series 64 32 32

Trace form

\( 464 q - 892 q^{4} - 16 q^{9} + O(q^{10}) \) \( 464 q - 892 q^{4} - 16 q^{9} - 30 q^{10} - 214 q^{15} - 3292 q^{16} + 228 q^{19} - 72 q^{24} - 196 q^{25} + 634 q^{30} - 816 q^{31} + 1264 q^{36} + 476 q^{39} - 30 q^{40} - 1377 q^{45} + 1920 q^{46} - 122 q^{51} - 2268 q^{54} + 2302 q^{60} - 1392 q^{61} + 24152 q^{64} + 2772 q^{66} + 765 q^{75} + 2464 q^{79} - 3716 q^{81} + 1636 q^{85} - 4416 q^{94} + 3456 q^{96} - 3196 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)