↑

Properties

Label 735.4.b
Level $735$
Weight $4$
Character orbit 735.b
Rep. character $\chi_{735}(146,\cdot)$
Character field $\Q$
Dimension $160$
Sturm bound $448$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 735.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 352 160 192
Cusp forms 320 160 160
Eisenstein series 32 0 32

Trace form

\( 160 q - 640 q^{4} + 60 q^{9} + O(q^{10}) \) \( 160 q - 640 q^{4} + 60 q^{9} - 40 q^{15} + 2080 q^{16} + 364 q^{18} + 600 q^{22} + 4000 q^{25} - 280 q^{30} - 2248 q^{36} + 2632 q^{37} + 1536 q^{39} + 1912 q^{43} - 3888 q^{46} - 760 q^{51} - 608 q^{57} - 2976 q^{58} - 340 q^{60} - 2368 q^{64} - 2392 q^{67} - 1988 q^{72} - 2592 q^{78} - 520 q^{79} + 6844 q^{81} - 1440 q^{85} + 4656 q^{88} + 2304 q^{93} + 1808 q^{99} + O(q^{100}) \)

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

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