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Properties

Label 1681.2.g
Level $1681$
Weight $2$
Character orbit 1681.g
Rep. character $\chi_{1681}(207,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $936$
Sturm bound $287$

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Defining parameters

Level: \( N \) \(=\) \( 1681 = 41^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1681.g (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 41 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(287\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1681, [\chi])\).

Total New Old
Modular forms 1320 1240 80
Cusp forms 984 936 48
Eisenstein series 336 304 32

Trace form

\( 936 q + 10 q^{2} + 6 q^{3} + 200 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} + 10 q^{8} + O(q^{10}) \) \( 936 q + 10 q^{2} + 6 q^{3} + 200 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} + 10 q^{8} - 6 q^{10} + 16 q^{11} - 2 q^{12} - 14 q^{14} - 8 q^{15} - 100 q^{16} - 8 q^{17} - 16 q^{19} - 20 q^{20} + 10 q^{21} - 6 q^{22} - 12 q^{23} - 68 q^{24} + 88 q^{25} + 28 q^{26} + 6 q^{27} - 18 q^{28} - 40 q^{29} + 36 q^{30} + 16 q^{31} - 10 q^{33} + 16 q^{34} + 36 q^{35} + 40 q^{36} - 4 q^{37} - 46 q^{38} + 50 q^{39} + 44 q^{40} - 216 q^{42} + 48 q^{44} - 70 q^{46} + 12 q^{47} + 50 q^{48} + 30 q^{49} + 20 q^{51} - 20 q^{52} + 26 q^{53} - 68 q^{54} - 20 q^{55} - 106 q^{56} - 26 q^{57} + 20 q^{58} - 6 q^{59} - 76 q^{60} - 30 q^{61} + 10 q^{62} - 92 q^{63} - 110 q^{64} - 68 q^{65} - 18 q^{66} + 22 q^{67} + 20 q^{68} + 38 q^{69} + 20 q^{70} - 4 q^{71} + 102 q^{72} - 10 q^{74} - 4 q^{75} + 128 q^{76} + 20 q^{77} - 18 q^{78} + 2 q^{79} + 70 q^{80} + 292 q^{81} - 368 q^{83} + 30 q^{84} + 56 q^{85} - 106 q^{86} + 10 q^{87} - 10 q^{88} + 72 q^{89} + 70 q^{90} - 28 q^{92} + 6 q^{93} + 18 q^{94} + 40 q^{95} - 66 q^{96} + 22 q^{97} - 14 q^{98} - 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1681, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1681, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1681, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(41, [\chi])\)\(^{\oplus 2}\)