Properties

Label 1694.2.m
Level $1694$
Weight $2$
Character orbit 1694.m
Rep. character $\chi_{1694}(155,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $660$
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.m (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{11})\)
Sturm bound: \(528\)

Dimensions

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

Total New Old
Modular forms 2680 660 2020
Cusp forms 2600 660 1940
Eisenstein series 80 0 80

Trace form

\( 660q + 2q^{2} + 4q^{3} - 66q^{4} + 4q^{6} + 2q^{8} + 672q^{9} + O(q^{10}) \) \( 660q + 2q^{2} + 4q^{3} - 66q^{4} + 4q^{6} + 2q^{8} + 672q^{9} + 10q^{11} - 18q^{12} - 108q^{13} - 20q^{15} - 66q^{16} + 12q^{17} + 10q^{18} + 28q^{19} + 12q^{21} - 34q^{22} + 8q^{23} + 4q^{24} - 42q^{25} + 40q^{27} + 44q^{29} + 40q^{30} - 48q^{31} + 2q^{32} + 44q^{33} + 28q^{34} + 4q^{35} - 54q^{36} + 24q^{37} - 104q^{38} + 56q^{39} + 12q^{41} + 48q^{43} + 10q^{44} + 24q^{45} + 32q^{46} + 48q^{47} + 4q^{48} - 66q^{49} + 30q^{50} - 126q^{51} + 24q^{52} + 32q^{53} + 64q^{54} - 28q^{55} + 58q^{57} - 72q^{58} + 60q^{59} + 24q^{60} + 64q^{61} + 16q^{62} - 66q^{64} - 44q^{65} + 26q^{66} - 48q^{67} + 12q^{68} + 72q^{69} - 36q^{70} - 48q^{71} + 10q^{72} - 20q^{73} + 52q^{74} + 100q^{75} - 38q^{76} + 8q^{77} + 64q^{78} + 4q^{79} + 740q^{81} - 44q^{82} + 100q^{83} + 12q^{84} - 108q^{85} + 44q^{86} + 72q^{87} - 56q^{88} + 60q^{89} - 104q^{90} - 108q^{91} + 8q^{92} + 120q^{93} - 144q^{94} - 88q^{95} + 4q^{96} + 84q^{97} + 2q^{98} + 130q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1694, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(847, [\chi])\)\(^{\oplus 2}\)