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Properties

Label 1617.2.n
Level $1617$
Weight $2$
Character orbit 1617.n
Rep. character $\chi_{1617}(815,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $268$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 480 268 212
Cusp forms 416 268 148
Eisenstein series 64 0 64

Trace form

\( 268 q + 136 q^{4} + 4 q^{9} + O(q^{10}) \) \( 268 q + 136 q^{4} + 4 q^{9} + 30 q^{12} + 20 q^{15} - 140 q^{16} + 26 q^{18} - 6 q^{19} - 36 q^{24} - 138 q^{25} + 32 q^{30} + 54 q^{31} - 76 q^{36} + 26 q^{37} - 28 q^{39} - 60 q^{40} - 108 q^{43} + 54 q^{45} - 12 q^{46} + 24 q^{51} - 12 q^{52} - 66 q^{54} + 76 q^{57} + 12 q^{58} - 16 q^{60} + 36 q^{61} - 248 q^{64} + 30 q^{66} - 14 q^{67} - 52 q^{72} + 6 q^{73} - 72 q^{75} - 168 q^{78} - 42 q^{79} - 76 q^{81} + 84 q^{82} - 8 q^{85} - 18 q^{87} + 24 q^{88} - 22 q^{93} - 48 q^{94} + 18 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1617, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)