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Properties

Label 1617.2.bp
Level $1617$
Weight $2$
Character orbit 1617.bp
Rep. character $\chi_{1617}(64,\cdot)$
Character field $\Q(\zeta_{35})$
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.bp (of order \(35\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{35})\)
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

\( 2688 q + 112 q^{4} + 8 q^{5} + 4 q^{6} - 2 q^{7} + 112 q^{9} + O(q^{10}) \) \( 2688 q + 112 q^{4} + 8 q^{5} + 4 q^{6} - 2 q^{7} + 112 q^{9} - 24 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 30 q^{15} + 128 q^{16} + 6 q^{17} - 80 q^{19} - 64 q^{20} - 50 q^{22} + 32 q^{23} + 102 q^{24} + 144 q^{25} - 24 q^{26} - 74 q^{28} - 24 q^{29} - 12 q^{31} + 12 q^{33} + 152 q^{34} - 56 q^{35} + 112 q^{36} + 32 q^{37} - 40 q^{38} + 114 q^{40} - 48 q^{41} - 18 q^{42} + 8 q^{43} - 124 q^{44} - 20 q^{45} + 16 q^{46} + 78 q^{47} - 62 q^{49} + 60 q^{51} + 48 q^{52} + 28 q^{53} - 16 q^{54} - 102 q^{55} - 216 q^{56} + 10 q^{58} - 60 q^{60} + 36 q^{61} + 108 q^{62} - 2 q^{63} - 16 q^{64} + 24 q^{66} - 96 q^{67} - 32 q^{68} + 24 q^{69} + 28 q^{70} - 56 q^{71} + 78 q^{73} + 16 q^{75} - 64 q^{76} - 56 q^{77} + 24 q^{78} - 12 q^{79} - 220 q^{80} + 112 q^{81} + 24 q^{82} - 64 q^{83} - 12 q^{84} + 68 q^{85} + 154 q^{86} - 116 q^{87} + 204 q^{88} - 124 q^{89} + 16 q^{90} + 190 q^{91} + 38 q^{92} + 16 q^{93} + 320 q^{94} - 172 q^{95} - 92 q^{96} + 536 q^{97} - 464 q^{98} + 12 q^{99} + O(q^{100}) \)

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

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