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Properties

Label 882.4.m
Level $882$
Weight $4$
Character orbit 882.m
Rep. character $\chi_{882}(293,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $240$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(882, [\chi])\).

Total New Old
Modular forms 1040 240 800
Cusp forms 976 240 736
Eisenstein series 64 0 64

Trace form

\( 240 q + 480 q^{4} + 100 q^{9} + O(q^{10}) \) \( 240 q + 480 q^{4} + 100 q^{9} - 48 q^{11} + 72 q^{15} - 1920 q^{16} - 128 q^{18} - 192 q^{23} - 3000 q^{25} + 84 q^{29} - 328 q^{30} + 32 q^{36} + 672 q^{37} - 1756 q^{39} - 84 q^{43} + 1008 q^{46} - 1584 q^{50} - 2940 q^{51} - 8 q^{57} - 504 q^{58} + 672 q^{60} - 15360 q^{64} + 9240 q^{65} - 1176 q^{67} + 320 q^{72} - 2520 q^{74} - 5440 q^{78} - 1284 q^{79} - 4620 q^{81} - 1440 q^{85} - 2400 q^{86} - 768 q^{92} - 5256 q^{93} + 10020 q^{95} - 3232 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(882, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(882, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)