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Properties

Label 735.4.q
Level $735$
Weight $4$
Character orbit 735.q
Rep. character $\chi_{735}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
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 704 240 464
Cusp forms 640 240 400
Eisenstein series 64 0 64

Trace form

\( 240 q + 480 q^{4} + 8 q^{5} - 48 q^{6} + 1080 q^{9} + O(q^{10}) \) \( 240 q + 480 q^{4} + 8 q^{5} - 48 q^{6} + 1080 q^{9} - 18 q^{10} + 84 q^{11} + 84 q^{15} - 1864 q^{16} - 308 q^{19} + 952 q^{20} - 288 q^{24} - 182 q^{25} + 216 q^{26} + 352 q^{29} - 120 q^{30} + 1252 q^{31} + 48 q^{34} + 8640 q^{36} + 168 q^{39} + 438 q^{40} - 632 q^{41} + 1448 q^{44} - 72 q^{45} - 3452 q^{46} - 1208 q^{50} + 168 q^{51} - 216 q^{54} - 2084 q^{55} - 2192 q^{59} + 1518 q^{60} + 1592 q^{61} - 3712 q^{64} - 1628 q^{65} + 1740 q^{66} + 2112 q^{69} - 240 q^{71} + 308 q^{74} + 312 q^{75} - 4232 q^{76} + 2100 q^{79} + 5944 q^{80} - 9720 q^{81} - 12296 q^{85} + 2344 q^{86} - 3272 q^{89} - 324 q^{90} - 3092 q^{94} - 7584 q^{95} + 5268 q^{96} + 1512 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)