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Properties

Label 735.4.y
Level $735$
Weight $4$
Character orbit 735.y
Rep. character $\chi_{735}(128,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $928$
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.y (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 1408 992 416
Cusp forms 1280 928 352
Eisenstein series 128 64 64

Trace form

\( 928 q + 2 q^{3} + O(q^{10}) \) \( 928 q + 2 q^{3} + 28 q^{10} + 94 q^{12} + 16 q^{13} + 152 q^{15} + 6664 q^{16} + 98 q^{18} + 272 q^{22} + 148 q^{25} + 32 q^{27} + 1080 q^{30} + 296 q^{31} + 430 q^{33} + 1856 q^{36} - 428 q^{37} + 1296 q^{40} + 1312 q^{43} - 490 q^{45} - 1000 q^{46} - 1604 q^{48} + 532 q^{51} - 68 q^{52} - 1240 q^{55} - 6116 q^{57} + 2940 q^{58} + 634 q^{60} + 608 q^{61} + 92 q^{66} + 1012 q^{67} - 3766 q^{72} - 2804 q^{73} - 4086 q^{75} + 8256 q^{76} - 14944 q^{78} + 3824 q^{81} + 1112 q^{82} - 7520 q^{85} + 52 q^{87} - 2028 q^{88} + 5724 q^{90} - 4182 q^{93} + 1824 q^{96} - 7496 q^{97} + O(q^{100}) \)

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

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