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Properties

Label 1682.2.d
Level $1682$
Weight $2$
Character orbit 1682.d
Rep. character $\chi_{1682}(571,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $402$
Sturm bound $435$

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Defining parameters

Level: \( N \) \(=\) \( 1682 = 2 \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1682.d (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(435\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1682, [\chi])\).

Total New Old
Modular forms 1482 402 1080
Cusp forms 1122 402 720
Eisenstein series 360 0 360

Trace form

\( 402 q + q^{2} - 67 q^{4} + 4 q^{5} - 8 q^{6} + 4 q^{7} + q^{8} - 53 q^{9} + O(q^{10}) \) \( 402 q + q^{2} - 67 q^{4} + 4 q^{5} - 8 q^{6} + 4 q^{7} + q^{8} - 53 q^{9} + 10 q^{10} + 8 q^{11} - 12 q^{13} + 8 q^{14} + 18 q^{15} - 67 q^{16} + 22 q^{17} + 5 q^{18} + 12 q^{19} - 3 q^{20} - 2 q^{21} - 4 q^{22} - 28 q^{23} - 8 q^{24} - 81 q^{25} - 11 q^{26} - 48 q^{27} + 4 q^{28} - 92 q^{30} + 4 q^{31} + q^{32} - 24 q^{33} - 5 q^{34} - 4 q^{35} - 67 q^{36} - 18 q^{37} + 20 q^{38} + 20 q^{39} - 11 q^{40} + 42 q^{41} + 28 q^{42} + 12 q^{43} - 20 q^{44} + 29 q^{45} + 28 q^{46} + 30 q^{47} - 89 q^{49} - 5 q^{50} + 28 q^{51} + 16 q^{52} + 17 q^{53} + 18 q^{54} - 12 q^{55} + 8 q^{56} - 28 q^{57} - 12 q^{59} + 18 q^{60} - 26 q^{61} + 28 q^{62} + 6 q^{63} - 67 q^{64} + 17 q^{65} + 48 q^{66} - 2 q^{67} + 8 q^{68} + 8 q^{69} + 12 q^{70} - 18 q^{71} + 5 q^{72} + 17 q^{73} - 42 q^{74} - 24 q^{75} - 16 q^{76} - 22 q^{77} - 54 q^{78} + 60 q^{79} + 4 q^{80} - 127 q^{81} - 10 q^{82} + 6 q^{83} - 44 q^{84} - 12 q^{85} - 44 q^{86} - 4 q^{88} - 52 q^{89} + 24 q^{90} - 60 q^{91} - 28 q^{92} + 80 q^{93} - 18 q^{94} - 80 q^{95} + 6 q^{96} - q^{97} - 55 q^{98} - 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1682, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1682, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1682, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(841, [\chi])\)\(^{\oplus 2}\)