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Properties

Label 1617.2.by
Level $1617$
Weight $2$
Character orbit 1617.by
Rep. character $\chi_{1617}(13,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $2688$
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.by (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 5472 2688 2784
Cusp forms 5280 2688 2592
Eisenstein series 192 0 192

Trace form

\( 2688 q - 112 q^{4} - 10 q^{7} - 112 q^{9} + O(q^{10}) \) \( 2688 q - 112 q^{4} - 10 q^{7} - 112 q^{9} - 2 q^{11} - 12 q^{14} - 30 q^{15} + 96 q^{16} - 70 q^{17} - 112 q^{20} + 30 q^{22} + 32 q^{23} + 210 q^{24} - 128 q^{25} - 56 q^{26} + 30 q^{28} + 40 q^{29} - 224 q^{34} + 40 q^{35} + 112 q^{36} - 16 q^{37} - 56 q^{38} - 210 q^{40} + 30 q^{42} + 124 q^{44} + 28 q^{45} - 154 q^{47} - 6 q^{49} - 100 q^{51} + 68 q^{53} + 70 q^{55} + 88 q^{56} - 50 q^{58} + 56 q^{59} - 60 q^{60} - 140 q^{62} - 10 q^{63} - 288 q^{64} + 32 q^{67} + 68 q^{70} + 56 q^{71} - 210 q^{73} - 80 q^{74} - 48 q^{77} + 24 q^{78} - 60 q^{79} + 112 q^{81} - 60 q^{84} + 20 q^{85} + 238 q^{86} + 372 q^{88} - 28 q^{89} + 142 q^{91} - 38 q^{92} - 16 q^{93} + 560 q^{94} - 20 q^{95} - 12 q^{99} + O(q^{100}) \)

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

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