Properties

Label 441.4.f
Level $441$
Weight $4$
Character orbit 441.f
Rep. character $\chi_{441}(148,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $236$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 352 256 96
Cusp forms 320 236 84
Eisenstein series 32 20 12

Trace form

\( 236q - q^{2} + q^{3} - 451q^{4} + 7q^{5} - 19q^{6} + 18q^{8} - 43q^{9} + O(q^{10}) \) \( 236q - q^{2} + q^{3} - 451q^{4} + 7q^{5} - 19q^{6} + 18q^{8} - 43q^{9} - 12q^{10} - 72q^{11} - 112q^{12} - 11q^{13} - 167q^{15} - 1639q^{16} + 30q^{17} + 310q^{18} - 26q^{19} + 14q^{20} - 3q^{22} - 11q^{23} + 465q^{24} - 2377q^{25} - 1336q^{26} - 272q^{27} - 285q^{29} - 498q^{30} + 79q^{31} - 823q^{32} + 412q^{33} - 279q^{34} - 373q^{36} + 244q^{37} + 455q^{38} - 703q^{39} + 84q^{40} + 458q^{41} - 260q^{43} + 1822q^{44} + 367q^{45} + 552q^{46} + 411q^{47} + 497q^{48} - 69q^{50} + 757q^{51} + 148q^{52} + 484q^{53} - 3133q^{54} - 462q^{55} + 1431q^{57} + 534q^{58} + 120q^{59} + 2330q^{60} + 439q^{61} - 2076q^{62} + 9506q^{64} - 1503q^{65} - 2176q^{66} - 398q^{67} + 1839q^{68} - 2091q^{69} - 24q^{71} - 1731q^{72} - 1574q^{73} - 2218q^{74} + 5933q^{75} + 667q^{76} + 3252q^{78} - 803q^{79} + 4424q^{80} + 4385q^{81} + 3606q^{82} + 2457q^{83} - 1068q^{85} - 2759q^{86} - 1763q^{87} - 483q^{88} - 4808q^{89} + 4172q^{90} + 3794q^{92} - 2381q^{93} - 906q^{94} - 3782q^{95} - 800q^{96} - 1262q^{97} - 8197q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)