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Properties

Label 735.3.n
Level $735$
Weight $3$
Character orbit 735.n
Rep. character $\chi_{735}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $108$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 480 108 372
Cusp forms 416 108 308
Eisenstein series 64 0 64

Trace form

\( 108 q - 8 q^{2} - 6 q^{3} - 88 q^{4} - 16 q^{8} + 162 q^{9} + O(q^{10}) \) \( 108 q - 8 q^{2} - 6 q^{3} - 88 q^{4} - 16 q^{8} + 162 q^{9} - 72 q^{11} + 48 q^{12} - 128 q^{16} + 96 q^{17} + 24 q^{18} + 6 q^{19} - 8 q^{22} - 128 q^{23} - 108 q^{24} + 270 q^{25} - 156 q^{26} + 264 q^{29} + 18 q^{31} + 44 q^{32} - 528 q^{36} + 238 q^{37} - 240 q^{38} - 30 q^{39} - 108 q^{43} - 296 q^{44} - 260 q^{46} - 24 q^{47} - 80 q^{50} + 108 q^{51} + 492 q^{52} + 312 q^{53} - 492 q^{57} + 20 q^{58} + 324 q^{59} + 456 q^{61} + 48 q^{64} + 120 q^{65} - 108 q^{66} + 190 q^{67} + 204 q^{68} + 752 q^{71} - 24 q^{72} - 582 q^{73} - 112 q^{74} - 30 q^{75} - 24 q^{78} - 282 q^{79} - 480 q^{80} - 486 q^{81} - 684 q^{82} + 120 q^{85} - 156 q^{86} + 56 q^{88} - 96 q^{89} + 1832 q^{92} + 186 q^{93} - 60 q^{94} + 200 q^{95} + 432 q^{96} - 432 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)