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Properties

Label 1449.2.l
Level $1449$
Weight $2$
Character orbit 1449.l
Rep. character $\chi_{1449}(277,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $352$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 392 352 40
Cusp forms 376 352 24
Eisenstein series 16 0 16

Trace form

\( 352 q + 352 q^{4} - 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 352 q + 352 q^{4} - 2 q^{7} - 4 q^{9} + 4 q^{11} + 10 q^{12} + 2 q^{13} + 10 q^{14} + 2 q^{15} + 352 q^{16} - 6 q^{17} + 10 q^{18} - 4 q^{19} - 6 q^{21} - 20 q^{24} - 176 q^{25} - 24 q^{26} - 8 q^{28} - 8 q^{29} - 8 q^{30} - 16 q^{31} - 80 q^{32} - 20 q^{33} - 26 q^{35} - 36 q^{36} + 2 q^{37} - 10 q^{39} - 32 q^{41} - 60 q^{42} + 8 q^{43} - 6 q^{44} + 44 q^{45} + 80 q^{47} - 24 q^{48} - 2 q^{49} - 56 q^{50} + 24 q^{51} + 8 q^{52} + 20 q^{53} - 36 q^{54} - 24 q^{55} - 36 q^{56} + 4 q^{57} + 12 q^{58} + 96 q^{59} - 68 q^{60} - 28 q^{61} + 110 q^{63} + 352 q^{64} - 8 q^{65} - 72 q^{66} - 28 q^{67} - 34 q^{68} - 12 q^{70} + 12 q^{71} + 82 q^{72} - 28 q^{73} + 56 q^{74} + 18 q^{75} - 16 q^{76} - 24 q^{77} + 86 q^{78} - 52 q^{79} - 38 q^{80} - 12 q^{81} - 20 q^{83} - 8 q^{84} + 12 q^{85} + 6 q^{87} - 10 q^{89} - 60 q^{90} - 22 q^{91} - 32 q^{93} - 16 q^{95} - 84 q^{96} + 2 q^{97} - 104 q^{98} - 88 q^{99} + O(q^{100}) \)

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

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