Properties

Label 1694.2.i
Level $1694$
Weight $2$
Character orbit 1694.i
Rep. character $\chi_{1694}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
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.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 576 144 432
Cusp forms 480 144 336
Eisenstein series 96 0 96

Trace form

\( 144q + 72q^{4} + 12q^{5} + 64q^{9} + O(q^{10}) \) \( 144q + 72q^{4} + 12q^{5} + 64q^{9} + 8q^{14} + 8q^{15} - 72q^{16} - 16q^{23} + 80q^{25} + 36q^{26} + 12q^{31} + 128q^{36} + 12q^{37} - 12q^{38} - 4q^{42} + 108q^{45} - 36q^{47} - 12q^{49} + 32q^{53} + 4q^{56} + 8q^{58} - 60q^{59} + 4q^{60} - 144q^{64} - 8q^{67} - 68q^{70} - 8q^{71} - 84q^{75} - 12q^{80} - 80q^{81} + 24q^{82} - 28q^{86} - 108q^{89} - 116q^{91} - 32q^{92} - 20q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1694, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)