↑

Properties

Label 1694.2.bc
Level $1694$
Weight $2$
Character orbit 1694.bc
Rep. character $\chi_{1694}(25,\cdot)$
Character field $\Q(\zeta_{165})$
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.bc (of order \(165\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{165})\)
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

\( 7040 q - 88 q^{4} + 4 q^{5} + 8 q^{6} + 2 q^{7} + 892 q^{9} + O(q^{10}) \) \( 7040 q - 88 q^{4} + 4 q^{5} + 8 q^{6} + 2 q^{7} + 892 q^{9} - 2 q^{10} - 22 q^{11} + 8 q^{13} + 24 q^{14} - 100 q^{15} - 88 q^{16} - 2 q^{17} + 8 q^{18} - 8 q^{20} + 16 q^{21} - 88 q^{22} + 16 q^{23} - 4 q^{24} - 68 q^{25} - 8 q^{26} + 36 q^{27} + 14 q^{28} + 28 q^{29} - 8 q^{30} - 6 q^{31} - 46 q^{33} + 34 q^{35} + 192 q^{36} - 62 q^{37} + 4 q^{38} + 24 q^{39} + 34 q^{40} + 56 q^{41} + 2 q^{42} - 40 q^{43} - 10 q^{44} - 4 q^{45} - 4 q^{46} + 40 q^{47} - 134 q^{49} - 32 q^{50} + 36 q^{51} - 4 q^{52} - 54 q^{53} + 64 q^{54} + 20 q^{55} + 4 q^{56} + 24 q^{57} - 24 q^{58} + 12 q^{59} - 4 q^{60} + 34 q^{61} - 16 q^{62} + 120 q^{63} + 176 q^{64} - 56 q^{65} - 32 q^{66} + 72 q^{67} - 2 q^{68} - 168 q^{69} + 2 q^{70} - 8 q^{71} - 12 q^{72} + 6 q^{73} - 8 q^{74} - 28 q^{75} + 4 q^{76} - 94 q^{77} - 32 q^{78} - 98 q^{79} - 6 q^{80} + 808 q^{81} - 12 q^{82} - 80 q^{83} - 36 q^{84} - 396 q^{85} - 18 q^{86} - 112 q^{87} - 10 q^{88} - 158 q^{89} + 88 q^{90} + 36 q^{91} + 204 q^{92} - 96 q^{93} + 124 q^{94} + 250 q^{95} - 4 q^{96} + 136 q^{97} + 40 q^{98} + 380 q^{99} + O(q^{100}) \)

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

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