Properties

Label 1694.2.o
Level $1694$
Weight $2$
Character orbit 1694.o
Rep. character $\chi_{1694}(153,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $880$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1694.o (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2680 880 1800
Cusp forms 2600 880 1720
Eisenstein series 80 0 80

Trace form

\( 880q + 88q^{4} - 872q^{9} + O(q^{10}) \) \( 880q + 88q^{4} - 872q^{9} + 40q^{11} + 14q^{14} - 28q^{15} - 88q^{16} - 40q^{22} - 32q^{23} + 80q^{25} - 96q^{36} - 116q^{37} + 20q^{42} + 4q^{44} + 56q^{49} - 44q^{51} + 4q^{53} + 8q^{56} + 32q^{58} - 16q^{60} - 110q^{63} + 88q^{64} - 72q^{67} - 32q^{70} - 16q^{71} + 40q^{77} - 32q^{78} + 176q^{79} + 800q^{81} - 220q^{85} - 24q^{86} - 4q^{88} - 66q^{91} - 144q^{92} + 100q^{93} - 176q^{95} - 88q^{98} - 128q^{99} + O(q^{100}) \)

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

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