Properties

Label 1694.2.bb
Level $1694$
Weight $2$
Character orbit 1694.bb
Rep. character $\chi_{1694}(13,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $3520$
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.bb (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{110})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 10720 3520 7200
Cusp forms 10400 3520 6880
Eisenstein series 320 0 320

Trace form

\( 3520q - 88q^{4} - 10q^{7} + 892q^{9} + O(q^{10}) \) \( 3520q - 88q^{4} - 10q^{7} + 892q^{9} - 40q^{11} - 24q^{14} + 68q^{15} + 88q^{16} + 40q^{22} + 32q^{23} - 100q^{25} + 10q^{28} + 20q^{29} + 60q^{35} + 96q^{36} + 116q^{37} + 20q^{39} - 10q^{42} + 16q^{44} - 96q^{49} + 104q^{51} + 36q^{53} - 8q^{56} - 80q^{57} + 48q^{58} + 16q^{60} + 70q^{63} - 88q^{64} + 72q^{67} - 8q^{70} - 104q^{71} - 40q^{72} - 40q^{74} - 40q^{77} + 32q^{78} - 236q^{79} - 940q^{81} - 20q^{84} + 300q^{85} - 36q^{86} - 16q^{88} + 46q^{91} + 204q^{92} - 140q^{93} + 76q^{95} + 88q^{98} + 288q^{99} + O(q^{100}) \)

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

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