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Properties

Label 1617.2.ci
Level $1617$
Weight $2$
Character orbit 1617.ci
Rep. character $\chi_{1617}(5,\cdot)$
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.ci (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

\( 10560 q - 33 q^{3} + 138 q^{4} - 42 q^{6} - 68 q^{7} - 39 q^{9} + O(q^{10}) \) \( 10560 q - 33 q^{3} + 138 q^{4} - 42 q^{6} - 68 q^{7} - 39 q^{9} - 164 q^{10} - 100 q^{12} - 84 q^{13} - 18 q^{15} - 278 q^{16} - 34 q^{18} - 108 q^{19} - 106 q^{21} - 126 q^{22} + 9 q^{24} - 270 q^{25} + 21 q^{27} + 26 q^{28} - 6 q^{30} - 90 q^{31} - 116 q^{33} - 224 q^{34} - 14 q^{36} - 82 q^{37} - 23 q^{39} + 168 q^{40} + 184 q^{42} - 128 q^{43} - 94 q^{45} - 54 q^{46} - 140 q^{49} - 33 q^{51} - 54 q^{52} - 16 q^{54} - 322 q^{55} - 68 q^{57} + 214 q^{58} - 417 q^{60} - 66 q^{61} - 16 q^{63} - 484 q^{64} - 93 q^{66} - 128 q^{67} - 210 q^{69} - 82 q^{70} - 117 q^{72} - 114 q^{73} - 105 q^{75} - 112 q^{76} + 204 q^{78} + 93 q^{81} - 138 q^{82} - 449 q^{84} + 28 q^{85} - 438 q^{87} - 110 q^{88} + 28 q^{90} - 416 q^{91} - 42 q^{93} - 162 q^{94} + 101 q^{96} - 464 q^{99} + O(q^{100}) \)

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.