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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

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

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

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