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Properties

Label 1694.4.k
Level $1694$
Weight $4$
Character orbit 1694.k
Rep. character $\chi_{1694}(475,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $864$
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.k (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 3264 864 2400
Cusp forms 3072 864 2208
Eisenstein series 192 0 192

Trace form

\( 864 q + 864 q^{4} - 20 q^{7} + 1848 q^{9} + O(q^{10}) \) \( 864 q + 864 q^{4} - 20 q^{7} + 1848 q^{9} - 52 q^{14} + 372 q^{15} - 3456 q^{16} - 392 q^{23} + 6124 q^{25} - 120 q^{28} + 700 q^{29} - 1010 q^{35} - 8032 q^{36} + 552 q^{37} - 460 q^{39} + 740 q^{42} - 502 q^{49} - 3620 q^{51} + 1120 q^{53} + 128 q^{56} - 560 q^{57} - 1344 q^{58} + 992 q^{60} - 6440 q^{63} + 13824 q^{64} - 8032 q^{67} + 264 q^{70} + 3880 q^{71} + 2240 q^{72} + 2800 q^{74} + 4288 q^{78} + 4200 q^{79} - 11104 q^{81} + 400 q^{84} + 6940 q^{85} + 296 q^{86} - 9066 q^{91} - 1792 q^{92} - 20668 q^{93} + 1560 q^{95} + O(q^{100}) \)

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

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