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Properties

Label 882.4.v
Level $882$
Weight $4$
Character orbit 882.v
Rep. character $\chi_{882}(125,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
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.v (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 3072 336 2736
Cusp forms 2976 336 2640
Eisenstein series 96 0 96

Trace form

\( 336 q + 224 q^{4} - 40 q^{7} + O(q^{10}) \) \( 336 q + 224 q^{4} - 40 q^{7} - 896 q^{16} + 840 q^{22} - 1232 q^{25} + 160 q^{28} - 1036 q^{37} + 672 q^{40} - 728 q^{43} - 3320 q^{49} + 1456 q^{52} + 1092 q^{55} + 2520 q^{58} + 7756 q^{61} + 3584 q^{64} + 3416 q^{67} + 4248 q^{70} - 448 q^{79} - 7056 q^{85} + 1344 q^{88} + 6792 q^{91} + 4368 q^{94} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)