↑

Properties

Label 882.4.z
Level $882$
Weight $4$
Character orbit 882.z
Rep. character $\chi_{882}(37,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $840$
Sturm bound $672$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.z (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 6144 840 5304
Cusp forms 5952 840 5112
Eisenstein series 192 0 192

Trace form

\( 840 q + 280 q^{4} + 18 q^{5} + 8 q^{7} + O(q^{10}) \) \( 840 q + 280 q^{4} + 18 q^{5} + 8 q^{7} - 8 q^{10} - 210 q^{11} + 192 q^{13} + 72 q^{14} + 1120 q^{16} - 298 q^{17} + 220 q^{19} + 80 q^{20} + 476 q^{22} - 658 q^{23} + 1596 q^{25} - 412 q^{26} - 40 q^{28} - 14 q^{29} + 138 q^{31} + 512 q^{34} - 484 q^{35} + 1036 q^{37} + 1928 q^{38} - 704 q^{40} - 1568 q^{41} - 672 q^{43} - 840 q^{44} - 3472 q^{46} - 3224 q^{47} + 3964 q^{49} + 336 q^{50} + 176 q^{52} + 1246 q^{53} + 2084 q^{55} - 64 q^{56} - 840 q^{58} + 1464 q^{59} - 3052 q^{61} + 8 q^{62} - 8960 q^{64} - 896 q^{65} - 630 q^{67} - 1304 q^{68} + 4124 q^{70} + 5124 q^{71} + 1546 q^{73} - 2212 q^{74} + 368 q^{76} + 4410 q^{77} - 742 q^{79} - 832 q^{80} - 1200 q^{82} + 6000 q^{83} + 2436 q^{85} + 84 q^{86} - 560 q^{88} + 12554 q^{89} - 3962 q^{91} + 560 q^{92} + 1308 q^{94} - 9366 q^{95} - 9220 q^{97} + 3448 q^{98} + O(q^{100}) \)

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

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