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Properties

Label 1694.2.r
Level $1694$
Weight $2$
Character orbit 1694.r
Rep. character $\chi_{1694}(215,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $576$
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.r (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2304 576 1728
Cusp forms 1920 576 1344
Eisenstein series 384 0 384

Trace form

\( 576 q - 72 q^{4} - 12 q^{5} + 10 q^{7} - 84 q^{9} + O(q^{10}) \) \( 576 q - 72 q^{4} - 12 q^{5} + 10 q^{7} - 84 q^{9} + 2 q^{14} + 12 q^{15} + 72 q^{16} + 30 q^{17} + 16 q^{23} - 60 q^{25} + 24 q^{26} - 10 q^{28} - 20 q^{29} + 18 q^{31} - 30 q^{35} - 128 q^{36} - 12 q^{37} + 12 q^{38} - 20 q^{39} + 30 q^{40} - 6 q^{42} - 108 q^{45} + 36 q^{47} + 82 q^{49} + 60 q^{51} - 12 q^{53} - 4 q^{56} + 80 q^{57} + 32 q^{58} + 60 q^{59} - 4 q^{60} - 30 q^{61} - 50 q^{63} + 144 q^{64} + 48 q^{67} - 30 q^{68} + 18 q^{70} + 8 q^{71} - 20 q^{72} - 90 q^{73} - 20 q^{74} - 156 q^{75} - 160 q^{78} - 30 q^{79} - 18 q^{80} + 40 q^{81} - 84 q^{82} - 40 q^{84} - 140 q^{85} - 2 q^{86} - 12 q^{89} + 46 q^{91} - 28 q^{92} - 30 q^{93} + 120 q^{94} + 70 q^{95} + O(q^{100}) \)

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

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