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Properties

Label 441.4.u
Level $441$
Weight $4$
Character orbit 441.u
Rep. character $\chi_{441}(64,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $414$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Sturm bound: \(224\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(441, [\chi])\).

Total New Old
Modular forms 1032 426 606
Cusp forms 984 414 570
Eisenstein series 48 12 36

Trace form

\( 414 q + 5 q^{2} - 277 q^{4} + 7 q^{5} - 20 q^{7} - 53 q^{8} + O(q^{10}) \) \( 414 q + 5 q^{2} - 277 q^{4} + 7 q^{5} - 20 q^{7} - 53 q^{8} - 39 q^{10} - 93 q^{11} + 21 q^{13} - 231 q^{14} - 1101 q^{16} - 43 q^{17} + 516 q^{19} + 515 q^{20} + 739 q^{22} - 261 q^{23} - 1266 q^{25} - 381 q^{26} + 62 q^{28} + 243 q^{29} + 516 q^{31} + 141 q^{32} - 1365 q^{34} - 1071 q^{35} + 345 q^{37} + 665 q^{38} + 1961 q^{40} - 939 q^{41} - 33 q^{43} + 379 q^{44} + 2433 q^{46} + 1023 q^{47} - 1408 q^{49} + 6088 q^{50} - 2715 q^{52} - 331 q^{53} + 853 q^{55} + 854 q^{56} - 3 q^{58} - 1177 q^{59} + 4399 q^{61} - 3649 q^{62} - 1491 q^{64} + 707 q^{65} + 912 q^{67} - 5584 q^{68} + 6559 q^{70} + 3127 q^{71} - 521 q^{73} - 4505 q^{74} + 2014 q^{76} + 427 q^{77} + 436 q^{79} - 12464 q^{80} + 1212 q^{82} - 1131 q^{83} + 161 q^{85} + 633 q^{86} + 827 q^{88} + 7957 q^{89} - 1113 q^{91} + 6574 q^{92} + 224 q^{94} + 5222 q^{95} + 268 q^{97} + 10171 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

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