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Properties

Label 1617.2.cg
Level $1617$
Weight $2$
Character orbit 1617.cg
Rep. character $\chi_{1617}(2,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $10560$
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.cg (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1617 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(448\)

Dimensions

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

Total New Old
Modular forms 10944 10944 0
Cusp forms 10560 10560 0
Eisenstein series 384 384 0

Trace form

\( 10560 q - 39 q^{3} - 294 q^{4} - 50 q^{6} - 120 q^{7} - 39 q^{9} + O(q^{10}) \) \( 10560 q - 39 q^{3} - 294 q^{4} - 50 q^{6} - 120 q^{7} - 39 q^{9} - 96 q^{12} - 100 q^{13} - 42 q^{15} - 294 q^{16} - 30 q^{18} - 60 q^{19} - 14 q^{22} - 45 q^{24} + 114 q^{25} + 15 q^{27} - 150 q^{28} - 42 q^{31} - 48 q^{33} - 128 q^{34} - 54 q^{36} - 82 q^{37} - 65 q^{39} - 440 q^{40} - 188 q^{42} - 46 q^{45} - 90 q^{46} - 98 q^{48} - 140 q^{49} - 65 q^{51} - 130 q^{52} + 50 q^{55} - 130 q^{57} - 474 q^{58} + 287 q^{60} - 90 q^{61} - 130 q^{63} + 284 q^{64} - 35 q^{66} - 64 q^{67} + 48 q^{69} - 162 q^{70} - 125 q^{72} - 70 q^{73} - 31 q^{75} + 196 q^{78} - 60 q^{79} - 219 q^{81} - 78 q^{82} - 195 q^{84} - 180 q^{85} - 114 q^{88} - 100 q^{90} - 432 q^{91} - 54 q^{93} + 210 q^{94} - 205 q^{96} - 208 q^{97} + 284 q^{99} + O(q^{100}) \)

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.