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Properties

Label 1617.4.bj
Level $1617$
Weight $4$
Character orbit 1617.bj
Rep. character $\chi_{1617}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1920$
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.bj (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(896\)

Dimensions

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

Total New Old
Modular forms 5504 1920 3584
Cusp forms 5248 1920 3328
Eisenstein series 256 0 256

Trace form

\( 1920 q - 1000 q^{4} + 48 q^{5} - 320 q^{8} - 2160 q^{9} + O(q^{10}) \) \( 1920 q - 1000 q^{4} + 48 q^{5} - 320 q^{8} - 2160 q^{9} - 40 q^{11} - 252 q^{15} + 3536 q^{16} - 60 q^{17} - 180 q^{18} + 1688 q^{22} + 544 q^{23} - 1350 q^{24} - 5740 q^{25} - 912 q^{26} - 1400 q^{29} + 1242 q^{31} - 54 q^{33} - 18000 q^{36} - 228 q^{37} + 1488 q^{38} + 2160 q^{40} - 2868 q^{44} + 432 q^{45} + 5180 q^{46} + 912 q^{47} - 840 q^{51} - 3320 q^{53} + 1440 q^{58} + 2064 q^{59} + 2232 q^{60} - 4920 q^{61} + 23872 q^{64} + 2052 q^{66} - 4912 q^{67} + 720 q^{68} + 11392 q^{71} - 3060 q^{72} + 5760 q^{73} + 2800 q^{74} - 936 q^{75} - 2952 q^{78} + 2700 q^{79} + 10560 q^{80} + 19440 q^{81} + 9576 q^{82} - 20480 q^{85} - 16788 q^{86} + 1998 q^{88} - 5040 q^{89} - 1384 q^{92} + 4776 q^{93} - 18480 q^{94} - 2660 q^{95} + 2880 q^{99} + O(q^{100}) \)

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

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