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Properties

Label 735.3.f
Level $735$
Weight $3$
Character orbit 735.f
Rep. character $\chi_{735}(344,\cdot)$
Character field $\Q$
Dimension $154$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 735.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(735, [\chi])\).

Total New Old
Modular forms 240 174 66
Cusp forms 208 154 54
Eisenstein series 32 20 12

Trace form

\( 154 q + 290 q^{4} + 6 q^{6} + 2 q^{9} + O(q^{10}) \) \( 154 q + 290 q^{4} + 6 q^{6} + 2 q^{9} + 14 q^{10} + 6 q^{15} + 562 q^{16} - 28 q^{19} + 114 q^{24} - 2 q^{25} + 128 q^{30} + 36 q^{31} + 172 q^{34} + 90 q^{36} + 8 q^{39} + 110 q^{40} - 120 q^{45} + 20 q^{46} - 300 q^{51} - 6 q^{54} + 16 q^{55} + 22 q^{60} - 196 q^{61} + 1202 q^{64} - 284 q^{66} - 200 q^{69} - 204 q^{75} - 284 q^{76} - 292 q^{79} - 278 q^{81} - 156 q^{85} + 62 q^{90} - 780 q^{94} + 714 q^{96} - 840 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(735, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(735, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(735, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)