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Properties

Label 882.4.u
Level $882$
Weight $4$
Character orbit 882.u
Rep. character $\chi_{882}(127,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $420$
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.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 3072 420 2652
Cusp forms 2976 420 2556
Eisenstein series 96 0 96

Trace form

\( 420 q - 280 q^{4} + 6 q^{5} + 16 q^{7} + O(q^{10}) \) \( 420 q - 280 q^{4} + 6 q^{5} + 16 q^{7} + 44 q^{10} + 168 q^{11} + 30 q^{13} + 60 q^{14} - 1120 q^{16} + 160 q^{17} - 484 q^{19} - 200 q^{20} - 476 q^{22} + 448 q^{23} - 2058 q^{25} + 304 q^{26} + 64 q^{28} + 14 q^{29} + 780 q^{31} - 104 q^{34} + 940 q^{35} + 1358 q^{37} + 568 q^{38} - 160 q^{40} + 1064 q^{41} + 168 q^{43} - 504 q^{44} - 1652 q^{46} - 1018 q^{47} + 2726 q^{49} - 336 q^{50} + 64 q^{52} - 1036 q^{53} - 572 q^{55} + 352 q^{56} - 1680 q^{58} + 1008 q^{59} - 5588 q^{61} + 2524 q^{62} - 4480 q^{64} - 1792 q^{65} + 252 q^{67} + 752 q^{68} - 3440 q^{70} - 5124 q^{71} - 1564 q^{73} + 3220 q^{74} - 872 q^{76} - 2292 q^{77} + 1036 q^{79} + 1216 q^{80} + 1320 q^{82} + 510 q^{83} - 2436 q^{85} + 1932 q^{86} + 1232 q^{88} - 9440 q^{89} - 3256 q^{91} - 560 q^{92} - 2076 q^{94} - 3444 q^{95} - 824 q^{97} - 5272 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(882, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)