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Properties

Label 1449.2.da
Level $1449$
Weight $2$
Character orbit 1449.da
Rep. character $\chi_{1449}(101,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $3760$
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.da (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1449 \)
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 3920 0
Cusp forms 3760 3760 0
Eisenstein series 160 160 0

Trace form

\( 3760 q - 27 q^{3} + 350 q^{4} - 27 q^{5} - 12 q^{6} - 9 q^{7} - q^{9} + O(q^{10}) \) \( 3760 q - 27 q^{3} + 350 q^{4} - 27 q^{5} - 12 q^{6} - 9 q^{7} - q^{9} - 54 q^{10} - 27 q^{11} - 39 q^{12} - 39 q^{14} - 46 q^{15} - 378 q^{16} - 5 q^{18} - 54 q^{19} - 12 q^{20} + 23 q^{21} - 48 q^{22} - 27 q^{23} - 54 q^{24} + 181 q^{25} + 12 q^{26} - 81 q^{27} - 32 q^{28} - 18 q^{29} - 53 q^{30} - 27 q^{33} - 12 q^{34} - 30 q^{35} - 16 q^{36} - 18 q^{37} - 87 q^{38} - 19 q^{39} - 81 q^{40} - 12 q^{41} + 10 q^{42} - 18 q^{43} + 102 q^{44} - 96 q^{45} - 18 q^{46} - 192 q^{47} + 96 q^{48} + 45 q^{49} + q^{51} + 21 q^{52} - 48 q^{53} - 3 q^{54} - 243 q^{56} + 6 q^{57} + q^{58} + 6 q^{59} - 13 q^{60} - 24 q^{62} + 101 q^{63} + 256 q^{64} + 114 q^{66} - 18 q^{67} - 60 q^{68} - 12 q^{69} - 40 q^{70} - 217 q^{72} - 54 q^{73} + 69 q^{74} - 3 q^{75} - 105 q^{77} - 130 q^{78} - 18 q^{79} + 24 q^{80} - 181 q^{81} - 66 q^{82} + 30 q^{84} - 28 q^{85} - 27 q^{86} - 57 q^{87} - 55 q^{88} + 84 q^{89} + 96 q^{90} - 52 q^{91} - 96 q^{92} - 70 q^{93} - 51 q^{96} + 90 q^{98} + 172 q^{99} + O(q^{100}) \)

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.