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Properties

Label 735.3.c
Level $735$
Weight $3$
Character orbit 735.c
Rep. character $\chi_{735}(491,\cdot)$
Character field $\Q$
Dimension $110$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
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 240 110 130
Cusp forms 208 110 98
Eisenstein series 32 0 32

Trace form

\( 110 q - 4 q^{3} - 226 q^{4} + 18 q^{6} - 22 q^{9} + O(q^{10}) \) \( 110 q - 4 q^{3} - 226 q^{4} + 18 q^{6} - 22 q^{9} + 10 q^{10} - 16 q^{12} - 32 q^{13} + 10 q^{15} + 474 q^{16} + 92 q^{18} + 20 q^{19} - 116 q^{22} - 158 q^{24} - 550 q^{25} + 104 q^{27} - 60 q^{30} + 108 q^{31} + 24 q^{33} + 156 q^{34} + 90 q^{36} + 44 q^{37} - 36 q^{39} + 30 q^{40} - 188 q^{43} - 80 q^{45} - 276 q^{46} + 96 q^{48} + 12 q^{51} + 120 q^{52} - 278 q^{54} - 60 q^{55} + 68 q^{57} + 308 q^{58} - 10 q^{60} - 108 q^{61} - 962 q^{64} + 300 q^{66} + 588 q^{67} - 284 q^{72} + 356 q^{73} + 20 q^{75} - 148 q^{76} + 240 q^{78} - 680 q^{79} - 242 q^{81} + 104 q^{82} - 140 q^{85} + 184 q^{87} - 180 q^{88} + 170 q^{90} - 156 q^{93} - 764 q^{94} + 30 q^{96} - 396 q^{97} - 240 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)