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Properties

Label 1449.2.cm
Level $1449$
Weight $2$
Character orbit 1449.cm
Rep. character $\chi_{1449}(113,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $2880$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1449.cm (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 207 \)
Character field: \(\Q(\zeta_{66})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1449, [\chi])\).

Total New Old
Modular forms 3920 2880 1040
Cusp forms 3760 2880 880
Eisenstein series 160 0 160

Trace form

\( 2880 q - 4 q^{3} - 144 q^{4} + 6 q^{6} + 4 q^{9} + O(q^{10}) \) \( 2880 q - 4 q^{3} - 144 q^{4} + 6 q^{6} + 4 q^{9} + 4 q^{12} - 44 q^{15} + 144 q^{16} + 30 q^{18} - 12 q^{23} - 240 q^{24} + 132 q^{25} + 68 q^{27} - 36 q^{29} + 44 q^{30} - 12 q^{31} - 36 q^{32} - 44 q^{33} + 38 q^{36} + 132 q^{40} - 48 q^{41} - 24 q^{46} + 48 q^{47} + 4 q^{48} - 144 q^{49} - 132 q^{50} + 18 q^{52} - 28 q^{54} - 24 q^{55} - 66 q^{57} + 18 q^{58} + 24 q^{59} - 220 q^{60} + 276 q^{64} - 176 q^{66} - 126 q^{69} + 72 q^{72} - 528 q^{74} + 68 q^{75} - 306 q^{78} - 212 q^{81} - 36 q^{82} - 198 q^{83} + 154 q^{84} + 56 q^{87} - 836 q^{90} - 150 q^{92} + 332 q^{93} + 18 q^{94} + 72 q^{95} + 256 q^{96} - 66 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1449, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1449, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1449, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(207, [\chi])\)\(^{\oplus 2}\)