Properties

Label 1617.2.ck
Level $1617$
Weight $2$
Character orbit 1617.ck
Rep. character $\chi_{1617}(40,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $5376$
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.ck (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
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 5376 5568
Cusp forms 10560 5376 5184
Eisenstein series 384 0 384

Trace form

\( 5376 q + 112 q^{4} - 12 q^{5} + 10 q^{7} + 112 q^{9} + O(q^{10}) \) \( 5376 q + 112 q^{4} - 12 q^{5} + 10 q^{7} + 112 q^{9} + 20 q^{11} - 12 q^{14} + 30 q^{15} - 120 q^{16} + 130 q^{17} + 112 q^{20} - 30 q^{22} + 16 q^{23} - 120 q^{24} + 104 q^{25} + 32 q^{26} - 30 q^{28} - 40 q^{29} + 18 q^{31} - 18 q^{33} + 224 q^{34} + 80 q^{35} + 224 q^{36} - 8 q^{37} - 88 q^{38} - 330 q^{40} + 42 q^{42} + 188 q^{44} + 44 q^{45} + 94 q^{47} - 18 q^{49} - 260 q^{51} + 76 q^{53} - 28 q^{55} + 440 q^{56} - 4 q^{58} - 104 q^{59} - 156 q^{60} - 30 q^{61} - 280 q^{62} + 10 q^{63} - 48 q^{64} - 36 q^{66} + 16 q^{67} - 180 q^{68} - 188 q^{70} - 56 q^{71} + 120 q^{73} - 40 q^{74} + 24 q^{75} - 42 q^{77} - 24 q^{78} - 30 q^{79} - 228 q^{80} - 112 q^{81} - 168 q^{82} + 60 q^{84} - 20 q^{85} - 322 q^{86} - 66 q^{88} - 308 q^{89} - 244 q^{91} + 164 q^{92} - 8 q^{93} - 560 q^{94} - 10 q^{95} + 12 q^{99} + O(q^{100}) \)

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

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