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Properties

Label 1617.2.i
Level $1617$
Weight $2$
Character orbit 1617.i
Rep. character $\chi_{1617}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $132$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 480 132 348
Cusp forms 416 132 284
Eisenstein series 64 0 64

Trace form

\( 132 q - 2 q^{3} - 64 q^{4} - 24 q^{8} - 66 q^{9} + O(q^{10}) \) \( 132 q - 2 q^{3} - 64 q^{4} - 24 q^{8} - 66 q^{9} + 12 q^{10} - 4 q^{12} - 12 q^{13} - 52 q^{16} + 6 q^{19} + 32 q^{20} - 16 q^{23} - 78 q^{25} + 4 q^{26} + 4 q^{27} + 16 q^{29} + 16 q^{30} - 22 q^{31} + 44 q^{32} - 4 q^{33} - 24 q^{34} + 128 q^{36} + 30 q^{37} - 12 q^{38} + 26 q^{39} + 12 q^{40} + 32 q^{41} - 12 q^{43} + 8 q^{44} + 24 q^{46} + 28 q^{47} - 16 q^{48} - 224 q^{50} - 16 q^{51} + 8 q^{52} + 36 q^{53} + 32 q^{55} - 68 q^{57} + 56 q^{58} + 32 q^{59} - 4 q^{60} - 8 q^{61} + 88 q^{62} + 96 q^{64} + 32 q^{65} - 8 q^{66} + 42 q^{67} - 36 q^{68} + 24 q^{69} + 16 q^{71} + 12 q^{72} + 30 q^{73} + 16 q^{74} - 6 q^{75} - 120 q^{76} + 48 q^{78} - 10 q^{79} + 16 q^{80} - 66 q^{81} + 32 q^{83} - 168 q^{85} + 20 q^{86} + 12 q^{87} - 24 q^{88} + 20 q^{89} - 24 q^{90} - 16 q^{92} + 26 q^{93} + 52 q^{94} - 72 q^{95} + 20 q^{96} + 128 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1617, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 2}\)