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Properties

Label 1617.4.c
Level $1617$
Weight $4$
Character orbit 1617.c
Rep. character $\chi_{1617}(538,\cdot)$
Character field $\Q$
Dimension $240$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1617.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1617, [\chi])\).

Total New Old
Modular forms 688 240 448
Cusp forms 656 240 416
Eisenstein series 32 0 32

Trace form

\( 240 q - 1000 q^{4} - 2160 q^{9} + O(q^{10}) \) \( 240 q - 1000 q^{4} - 2160 q^{9} - 40 q^{11} + 168 q^{15} + 4168 q^{16} - 676 q^{22} + 880 q^{23} - 6808 q^{25} + 9000 q^{36} - 904 q^{37} + 1248 q^{44} + 3632 q^{53} - 2488 q^{58} - 792 q^{60} - 12456 q^{64} - 3792 q^{67} + 2528 q^{71} - 3456 q^{78} + 19440 q^{81} + 272 q^{86} + 10716 q^{88} + 1632 q^{92} - 4080 q^{93} + 360 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1617, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1617, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1617, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)