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Properties

Label 1617.2.t
Level $1617$
Weight $2$
Character orbit 1617.t
Rep. character $\chi_{1617}(50,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $616$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1617.t (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1617, [\chi])\).

Total New Old
Modular forms 960 696 264
Cusp forms 832 616 216
Eisenstein series 128 80 48

Trace form

\( 616 q - 138 q^{4} + 10 q^{6} + 4 q^{9} + O(q^{10}) \) \( 616 q - 138 q^{4} + 10 q^{6} + 4 q^{9} + 8 q^{12} + 10 q^{13} - 18 q^{15} - 98 q^{16} + 10 q^{18} + 40 q^{19} - 72 q^{22} - 20 q^{24} + 96 q^{25} + 12 q^{27} + 50 q^{30} - 20 q^{31} + 48 q^{33} + 32 q^{34} + 6 q^{36} - 18 q^{37} - 50 q^{39} + 72 q^{45} + 130 q^{46} - 74 q^{48} - 40 q^{51} + 30 q^{52} + 4 q^{55} + 30 q^{57} - 52 q^{58} + 160 q^{60} - 30 q^{61} - 26 q^{64} - 88 q^{66} + 28 q^{67} - 10 q^{69} - 130 q^{72} - 40 q^{73} - 8 q^{75} - 112 q^{78} - 90 q^{79} + 8 q^{81} + 26 q^{82} - 70 q^{85} + 214 q^{88} - 140 q^{90} + 54 q^{93} + 30 q^{94} - 170 q^{96} + 82 q^{97} + 96 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1617, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1617, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1617, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)