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Properties

Label 882.4.l
Level $882$
Weight $4$
Character orbit 882.l
Rep. character $\chi_{882}(227,\cdot)$
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.l (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

\( 240 q - 960 q^{4} - 92 q^{9} + O(q^{10}) \) \( 240 q - 960 q^{4} - 92 q^{9} + 48 q^{11} - 72 q^{13} - 180 q^{15} + 3840 q^{16} - 144 q^{17} - 128 q^{18} - 564 q^{23} - 3000 q^{25} - 120 q^{26} + 450 q^{27} - 42 q^{29} - 496 q^{30} + 368 q^{36} + 168 q^{37} + 206 q^{39} + 618 q^{41} + 42 q^{43} - 192 q^{44} - 366 q^{45} + 252 q^{46} - 396 q^{47} - 2592 q^{50} + 1032 q^{51} + 288 q^{52} - 1020 q^{53} - 180 q^{54} + 2176 q^{57} + 252 q^{58} + 3000 q^{59} + 720 q^{60} - 2952 q^{62} - 15360 q^{64} + 1200 q^{66} - 1176 q^{67} + 576 q^{68} - 1848 q^{69} + 512 q^{72} - 1260 q^{74} + 534 q^{75} - 5104 q^{78} + 4332 q^{79} - 852 q^{81} - 1440 q^{85} + 2400 q^{86} + 4344 q^{87} + 4398 q^{89} + 6084 q^{90} + 2256 q^{92} - 2688 q^{93} - 1584 q^{97} + 2816 q^{99} + O(q^{100}) \)

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

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