Properties

Label 441.4.bb
Level $441$
Weight $4$
Character orbit 441.bb
Rep. character $\chi_{441}(37,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $828$
Sturm bound $224$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.bb (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(224\)

Dimensions

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

Total New Old
Modular forms 2064 852 1212
Cusp forms 1968 828 1140
Eisenstein series 96 24 72

Trace form

\( 828q + 13q^{2} + 259q^{4} - q^{5} - 10q^{7} + 68q^{8} + O(q^{10}) \) \( 828q + 13q^{2} + 259q^{4} - q^{5} - 10q^{7} + 68q^{8} - 24q^{10} + 111q^{11} - 186q^{13} - 39q^{14} + 1023q^{16} + 127q^{17} - 486q^{19} + 382q^{20} - 754q^{22} + 321q^{23} + 1794q^{25} + 108q^{26} + 304q^{28} - 228q^{29} - 1290q^{31} - 1659q^{32} + 402q^{34} + 1113q^{35} - 2001q^{37} - 1526q^{38} + 2110q^{40} + 1698q^{41} + 270q^{43} + 5390q^{44} + 3828q^{46} + 1521q^{47} - 2240q^{49} - 6052q^{50} - 3882q^{52} - 1037q^{53} - 3790q^{55} - 1928q^{56} - 12q^{58} - 827q^{59} - 445q^{61} + 430q^{62} - 10428q^{64} + 364q^{65} + 834q^{67} + 3607q^{68} - 8398q^{70} - 3112q^{71} + 629q^{73} + 1604q^{74} - 445q^{76} - 355q^{77} + 848q^{79} + 3182q^{80} - 13890q^{82} - 3258q^{83} - 176q^{85} - 471q^{86} + 5545q^{88} - 6529q^{89} + 8280q^{91} - 7966q^{92} + 9814q^{94} + 9328q^{95} + 4052q^{97} + 13415q^{98} + O(q^{100}) \)

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

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