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Properties

Label 1617.2.p
Level $1617$
Weight $2$
Character orbit 1617.p
Rep. character $\chi_{1617}(472,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 480 160 320
Cusp forms 416 160 256
Eisenstein series 64 0 64

Trace form

\( 160 q + 88 q^{4} + 12 q^{5} + 80 q^{9} + O(q^{10}) \) \( 160 q + 88 q^{4} + 12 q^{5} + 80 q^{9} + 2 q^{11} - 8 q^{15} - 80 q^{16} - 32 q^{23} + 104 q^{25} + 24 q^{26} + 12 q^{31} + 18 q^{33} + 176 q^{36} + 56 q^{37} - 24 q^{38} + 36 q^{44} + 12 q^{45} - 24 q^{47} - 52 q^{53} - 24 q^{58} + 48 q^{59} + 12 q^{60} - 296 q^{64} + 36 q^{66} - 44 q^{67} - 88 q^{71} - 24 q^{75} + 72 q^{78} - 72 q^{80} - 80 q^{81} + 48 q^{82} + 128 q^{86} + 72 q^{88} - 60 q^{89} - 336 q^{92} - 40 q^{93} + 4 q^{99} + O(q^{100}) \)

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

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