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Properties

Label 1441.2.bl
Level $1441$
Weight $2$
Character orbit 1441.bl
Rep. character $\chi_{1441}(12,\cdot)$
Character field $\Q(\zeta_{65})$
Dimension $5280$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.bl (of order \(65\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 131 \)
Character field: \(\Q(\zeta_{65})\)
Sturm bound: \(264\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1441, [\chi])\).

Total New Old
Modular forms 6432 5280 1152
Cusp forms 6240 5280 960
Eisenstein series 192 0 192

Trace form

\( 5280 q + 110 q^{4} + 12 q^{6} - 114 q^{8} + 110 q^{9} + O(q^{10}) \) \( 5280 q + 110 q^{4} + 12 q^{6} - 114 q^{8} + 110 q^{9} - 18 q^{10} - 48 q^{12} - 68 q^{14} + 16 q^{15} + 110 q^{16} - 32 q^{17} - 114 q^{18} - 16 q^{19} - 30 q^{20} + 2 q^{22} - 30 q^{23} + 72 q^{24} + 110 q^{25} - 90 q^{26} - 168 q^{27} - 194 q^{28} - 34 q^{29} + 30 q^{30} + 4 q^{31} + 128 q^{32} - 48 q^{34} - 56 q^{35} + 162 q^{36} + 8 q^{37} - 138 q^{38} + 56 q^{39} - 24 q^{40} - 24 q^{41} - 474 q^{42} + 20 q^{43} - 64 q^{45} - 16 q^{46} - 40 q^{47} - 442 q^{48} + 102 q^{49} - 100 q^{50} - 296 q^{51} + 72 q^{52} + 2 q^{53} + 56 q^{54} + 52 q^{56} - 368 q^{57} + 66 q^{58} - 58 q^{59} - 196 q^{60} + 12 q^{61} - 168 q^{62} + 100 q^{63} - 16 q^{64} - 288 q^{65} + 8 q^{66} - 76 q^{67} - 212 q^{68} - 20 q^{69} - 150 q^{70} - 92 q^{71} - 156 q^{72} + 50 q^{73} + 8 q^{74} - 144 q^{75} - 286 q^{76} - 6 q^{77} - 60 q^{78} - 104 q^{79} - 276 q^{80} + 150 q^{81} - 160 q^{82} - 214 q^{83} + 124 q^{84} - 70 q^{85} + 124 q^{86} - 484 q^{87} + 6 q^{88} + 4 q^{89} - 56 q^{90} - 16 q^{91} - 546 q^{92} - 44 q^{93} + 100 q^{94} - 212 q^{95} - 292 q^{96} + 10 q^{97} - 120 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1441, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1441, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1441, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(131, [\chi])\)\(^{\oplus 2}\)