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Properties

Label 1441.2.bc
Level $1441$
Weight $2$
Character orbit 1441.bc
Rep. character $\chi_{1441}(45,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $1320$
Sturm bound $264$

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Defining parameters

Level: \( N \) \(=\) \( 1441 = 11 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1441.bc (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 131 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(264\)

Dimensions

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

Total New Old
Modular forms 1608 1320 288
Cusp forms 1560 1320 240
Eisenstein series 48 0 48

Trace form

\( 1320 q - 110 q^{4} - 12 q^{6} + 54 q^{8} - 110 q^{9} + O(q^{10}) \) \( 1320 q - 110 q^{4} - 12 q^{6} + 54 q^{8} - 110 q^{9} - 12 q^{10} - 32 q^{12} + 38 q^{14} - 16 q^{15} - 110 q^{16} + 22 q^{17} + 54 q^{18} - 4 q^{19} - 40 q^{20} - 2 q^{22} - 10 q^{23} - 72 q^{24} - 110 q^{25} + 30 q^{26} + 108 q^{27} + 144 q^{28} + 14 q^{29} - 140 q^{30} - 24 q^{31} - 128 q^{32} - 32 q^{34} - 4 q^{35} - 162 q^{36} - 8 q^{37} + 58 q^{38} - 56 q^{39} - 56 q^{40} - 36 q^{41} + 324 q^{42} - 20 q^{43} - 16 q^{45} - 44 q^{46} - 60 q^{47} + 202 q^{48} - 122 q^{49} + 96 q^{51} - 72 q^{52} - 32 q^{53} - 56 q^{54} - 172 q^{56} + 248 q^{57} - 116 q^{58} - 12 q^{59} + 196 q^{60} - 12 q^{61} - 132 q^{62} - 100 q^{63} - 104 q^{64} + 98 q^{65} - 8 q^{66} + 36 q^{67} - 108 q^{68} - 60 q^{69} - 80 q^{70} - 48 q^{71} - 304 q^{72} - 60 q^{73} - 68 q^{74} - 36 q^{75} + 286 q^{76} - 4 q^{77} + 20 q^{78} - 56 q^{79} + 216 q^{80} - 190 q^{81} - 70 q^{82} + 144 q^{83} - 124 q^{84} + 10 q^{85} - 224 q^{86} + 384 q^{87} - 6 q^{88} - 4 q^{89} - 224 q^{90} - 64 q^{91} + 366 q^{92} - 116 q^{93} - 100 q^{94} + 42 q^{95} + 162 q^{96} - 40 q^{97} + 90 q^{98} + O(q^{100}) \)

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

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