↑

Properties

Label 1694.2.be
Level $1694$
Weight $2$
Character orbit 1694.be
Rep. character $\chi_{1694}(17,\cdot)$
Character field $\Q(\zeta_{330})$
Dimension $7040$
Sturm bound $528$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1694.be (of order \(330\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{330})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1694, [\chi])\).

Total New Old
Modular forms 21440 7040 14400
Cusp forms 20800 7040 13760
Eisenstein series 640 0 640

Trace form

\( 7040 q + 88 q^{4} - 12 q^{5} + 10 q^{7} - 892 q^{9} + O(q^{10}) \) \( 7040 q + 88 q^{4} - 12 q^{5} + 10 q^{7} - 892 q^{9} + 66 q^{10} - 14 q^{11} + 24 q^{14} + 100 q^{15} - 88 q^{16} + 30 q^{17} + 80 q^{22} + 16 q^{23} + 100 q^{25} + 24 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{31} + 126 q^{33} - 30 q^{35} + 192 q^{36} + 46 q^{37} + 12 q^{38} - 20 q^{39} + 30 q^{40} + 10 q^{42} + 2 q^{44} - 108 q^{45} + 12 q^{47} - 102 q^{49} + 16 q^{51} + 18 q^{53} - 4 q^{56} + 80 q^{57} + 24 q^{58} + 60 q^{59} - 4 q^{60} - 30 q^{61} - 160 q^{63} - 176 q^{64} - 72 q^{66} - 72 q^{67} - 30 q^{68} + 2 q^{70} + 8 q^{71} - 20 q^{72} - 90 q^{73} - 20 q^{74} - 204 q^{75} - 134 q^{77} - 32 q^{78} - 118 q^{79} - 18 q^{80} + 832 q^{81} - 36 q^{82} - 40 q^{84} + 300 q^{85} - 18 q^{86} - 14 q^{88} - 378 q^{89} - 148 q^{91} - 204 q^{92} - 136 q^{93} + 120 q^{94} - 106 q^{95} - 88 q^{98} - 324 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1694, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1694, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1694, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)