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Properties

Label 1694.4.x
Level $1694$
Weight $4$
Character orbit 1694.x
Rep. character $\chi_{1694}(87,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $5280$
Sturm bound $1056$

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Defining parameters

Level: \( N \) \(=\) \( 1694 = 2 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1694.x (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(1056\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1694, [\chi])\).

Total New Old
Modular forms 15920 5280 10640
Cusp forms 15760 5280 10480
Eisenstein series 160 0 160

Trace form

\( 5280 q - 1056 q^{4} - 48 q^{5} + 23824 q^{9} + O(q^{10}) \) \( 5280 q - 1056 q^{4} - 48 q^{5} + 23824 q^{9} - 396 q^{10} + 302 q^{11} + 188 q^{14} - 888 q^{15} + 4224 q^{16} + 1552 q^{22} + 196 q^{23} - 6980 q^{25} + 696 q^{26} + 828 q^{31} - 1314 q^{33} - 18496 q^{36} + 1728 q^{37} - 744 q^{38} + 552 q^{42} + 24 q^{44} - 3552 q^{45} - 1464 q^{47} - 7672 q^{49} + 572 q^{51} - 3598 q^{53} + 224 q^{56} - 672 q^{58} + 3000 q^{59} - 16 q^{60} + 6380 q^{63} + 33792 q^{64} + 384 q^{66} - 4176 q^{67} + 1752 q^{70} + 3200 q^{71} + 12744 q^{75} - 3770 q^{77} - 448 q^{78} + 3696 q^{79} + 768 q^{80} - 210712 q^{81} + 1104 q^{82} + 16544 q^{85} - 168 q^{86} - 64 q^{88} + 34020 q^{89} - 3932 q^{91} - 7056 q^{92} + 8152 q^{93} - 15136 q^{95} + 4048 q^{98} + 19448 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1694, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1694, [\chi])\) into lower level spaces

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