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Properties

Label 1694.4.c
Level $1694$
Weight $4$
Character orbit 1694.c
Rep. character $\chi_{1694}(1693,\cdot)$
Character field $\Q$
Dimension $216$
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Sturm bound: \(1056\)

Dimensions

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

Total New Old
Modular forms 816 216 600
Cusp forms 768 216 552
Eisenstein series 48 0 48

Trace form

\( 216 q - 864 q^{4} - 2008 q^{9} + O(q^{10}) \) \( 216 q - 864 q^{4} - 2008 q^{9} + 32 q^{14} + 248 q^{15} + 3456 q^{16} + 392 q^{23} - 5944 q^{25} + 8032 q^{36} - 552 q^{37} - 600 q^{42} + 1572 q^{49} + 2520 q^{53} - 128 q^{56} - 2016 q^{58} - 992 q^{60} - 13824 q^{64} - 3168 q^{67} - 1104 q^{70} + 760 q^{71} + 1632 q^{78} + 22904 q^{81} - 1136 q^{86} + 7376 q^{91} - 1568 q^{92} + 7768 q^{93} + O(q^{100}) \)

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

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