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Properties

Label 1449.2.n
Level $1449$
Weight $2$
Character orbit 1449.n
Rep. character $\chi_{1449}(668,\cdot)$
Character field $\Q(\zeta_{6})$
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.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 392 352 40
Cusp forms 376 352 24
Eisenstein series 16 0 16

Trace form

\( 352 q - 352 q^{4} + 2 q^{7} - 4 q^{9} + O(q^{10}) \) \( 352 q - 352 q^{4} + 2 q^{7} - 4 q^{9} + 12 q^{11} + 30 q^{12} + 6 q^{13} - 30 q^{14} - 10 q^{15} + 352 q^{16} - 18 q^{17} - 10 q^{18} - 6 q^{21} - 176 q^{25} + 36 q^{27} - 8 q^{28} - 32 q^{30} + 30 q^{35} - 4 q^{36} - 2 q^{37} - 22 q^{39} + 16 q^{42} - 8 q^{43} + 18 q^{44} - 48 q^{45} - 60 q^{48} - 2 q^{49} - 48 q^{50} - 72 q^{51} - 24 q^{52} - 84 q^{54} + 60 q^{56} + 4 q^{57} + 12 q^{58} + 116 q^{60} + 72 q^{62} - 14 q^{63} - 352 q^{64} + 48 q^{66} - 28 q^{67} + 42 q^{68} - 12 q^{70} + 2 q^{72} - 18 q^{75} - 24 q^{77} - 54 q^{78} + 44 q^{79} - 114 q^{80} - 28 q^{81} - 60 q^{83} - 160 q^{84} - 12 q^{85} - 120 q^{86} + 30 q^{87} - 30 q^{89} + 72 q^{90} - 6 q^{91} - 84 q^{96} + 6 q^{97} - 48 q^{98} + 24 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1449, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)