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Properties

Label 735.3.bc
Level $735$
Weight $3$
Character orbit 735.bc
Rep. character $\chi_{735}(34,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $672$
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.bc (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(336\)

Dimensions

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

Total New Old
Modular forms 1368 672 696
Cusp forms 1320 672 648
Eisenstein series 48 0 48

Trace form

\( 672 q + 224 q^{4} - 336 q^{9} + O(q^{10}) \) \( 672 q + 224 q^{4} - 336 q^{9} - 84 q^{11} + 84 q^{14} + 60 q^{15} - 496 q^{16} + 112 q^{20} + 12 q^{21} + 12 q^{25} + 224 q^{26} - 8 q^{29} + 48 q^{30} + 56 q^{34} + 4 q^{35} + 672 q^{36} + 180 q^{39} + 728 q^{40} - 196 q^{41} + 360 q^{44} + 42 q^{45} + 104 q^{46} + 124 q^{49} - 188 q^{50} + 60 q^{51} - 504 q^{55} + 228 q^{56} - 700 q^{59} - 180 q^{60} + 364 q^{61} + 752 q^{64} + 228 q^{65} + 490 q^{70} - 744 q^{71} - 120 q^{74} + 420 q^{76} - 296 q^{79} - 1008 q^{81} - 228 q^{84} + 144 q^{85} - 1472 q^{86} + 144 q^{91} + 112 q^{94} + 468 q^{95} + 168 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(735, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 2}\)