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

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

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

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