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Properties

Label 1449.2.m
Level $1449$
Weight $2$
Character orbit 1449.m
Rep. character $\chi_{1449}(137,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $376$
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.m (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1449 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 392 392 0
Cusp forms 376 376 0
Eisenstein series 16 16 0

Trace form

\( 376 q - 2 q^{3} - 372 q^{4} - 12 q^{6} - 10 q^{9} + O(q^{10}) \) \( 376 q - 2 q^{3} - 372 q^{4} - 12 q^{6} - 10 q^{9} - 22 q^{12} - 4 q^{13} + 356 q^{16} - 10 q^{18} + 18 q^{23} + 36 q^{24} - 170 q^{25} - 12 q^{26} - 2 q^{27} + 24 q^{29} - 4 q^{31} + 30 q^{35} + 52 q^{36} - 36 q^{39} + 8 q^{46} - 10 q^{48} + 10 q^{49} - 18 q^{50} - 6 q^{52} - 26 q^{54} - 36 q^{55} + 10 q^{58} - 344 q^{64} + 4 q^{69} - 30 q^{70} + 30 q^{72} - 4 q^{73} - 34 q^{75} - 120 q^{77} + 72 q^{78} + 22 q^{81} - 8 q^{82} + 6 q^{85} - 116 q^{87} - 42 q^{92} - 116 q^{93} + 76 q^{94} - 126 q^{96} + 114 q^{98} + O(q^{100}) \)

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.