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Properties

Label 1682.2.e
Level $1682$
Weight $2$
Character orbit 1682.e
Rep. character $\chi_{1682}(63,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $408$
Sturm bound $435$

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Defining parameters

Level: \( N \) \(=\) \( 1682 = 2 \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1682.e (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 29 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(435\)

Dimensions

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

Total New Old
Modular forms 1488 408 1080
Cusp forms 1128 408 720
Eisenstein series 360 0 360

Trace form

\( 408 q + 68 q^{4} + 2 q^{5} + 12 q^{6} - 4 q^{7} + 74 q^{9} + O(q^{10}) \) \( 408 q + 68 q^{4} + 2 q^{5} + 12 q^{6} - 4 q^{7} + 74 q^{9} + 26 q^{13} + 14 q^{15} - 68 q^{16} - 2 q^{20} - 14 q^{21} - 4 q^{22} + 16 q^{23} - 12 q^{24} - 92 q^{25} - 14 q^{26} + 4 q^{28} - 52 q^{30} - 28 q^{31} + 4 q^{33} + 4 q^{34} - 4 q^{35} - 88 q^{36} + 28 q^{37} - 28 q^{38} - 28 q^{39} + 14 q^{40} + 4 q^{42} + 28 q^{43} + 28 q^{44} + 10 q^{45} + 14 q^{47} - 62 q^{49} + 28 q^{50} - 4 q^{51} + 2 q^{52} - 22 q^{53} + 38 q^{54} - 28 q^{55} + 68 q^{57} + 36 q^{59} + 14 q^{60} + 28 q^{61} - 12 q^{62} - 30 q^{63} + 68 q^{64} + 4 q^{65} + 14 q^{67} + 14 q^{68} + 28 q^{69} - 38 q^{71} - 42 q^{73} - 28 q^{76} - 14 q^{77} + 22 q^{78} - 28 q^{79} + 2 q^{80} - 88 q^{81} + 20 q^{82} + 2 q^{83} - 28 q^{85} - 52 q^{86} + 4 q^{88} - 14 q^{89} - 70 q^{90} + 4 q^{91} - 16 q^{92} - 80 q^{93} + 10 q^{94} - 2 q^{96} + 28 q^{97} + O(q^{100}) \)

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

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