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Properties

Label 735.4.bo
Level $735$
Weight $4$
Character orbit 735.bo
Rep. character $\chi_{735}(4,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $2016$
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.bo (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(735, [\chi])\).

Total New Old
Modular forms 4080 2016 2064
Cusp forms 3984 2016 1968
Eisenstein series 96 0 96

Trace form

\( 2016 q - 672 q^{4} + 8 q^{5} - 48 q^{6} - 1512 q^{9} + O(q^{10}) \) \( 2016 q - 672 q^{4} + 8 q^{5} - 48 q^{6} - 1512 q^{9} - 18 q^{10} + 476 q^{11} - 84 q^{14} - 210 q^{15} + 2744 q^{16} + 1820 q^{19} + 56 q^{20} - 48 q^{21} - 288 q^{24} - 238 q^{25} - 848 q^{26} + 224 q^{29} - 168 q^{30} - 3956 q^{31} + 3688 q^{34} + 1064 q^{35} - 12096 q^{36} - 2184 q^{39} - 1074 q^{40} - 184 q^{41} + 8400 q^{44} + 936 q^{45} - 812 q^{46} + 2092 q^{49} + 8932 q^{50} - 2184 q^{51} - 216 q^{54} - 3722 q^{55} - 1428 q^{56} - 1828 q^{59} - 6762 q^{60} + 7640 q^{61} + 24640 q^{64} + 252 q^{65} + 1740 q^{66} + 2112 q^{69} - 1044 q^{70} + 1344 q^{71} + 7980 q^{74} + 312 q^{75} - 8516 q^{76} - 924 q^{79} - 2834 q^{80} + 13608 q^{81} - 6012 q^{84} - 4144 q^{85} + 1064 q^{86} - 3272 q^{89} - 324 q^{90} + 8108 q^{91} - 5276 q^{94} + 16464 q^{95} + 5268 q^{96} + 1512 q^{99} + O(q^{100}) \)

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

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