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Properties

Label 1449.2.db
Level $1449$
Weight $2$
Character orbit 1449.db
Rep. character $\chi_{1449}(11,\cdot)$
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.db (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

\( 3760 q - 9 q^{3} + 350 q^{4} - 33 q^{5} - 32 q^{6} - 11 q^{7} - q^{9} + O(q^{10}) \) \( 3760 q - 9 q^{3} + 350 q^{4} - 33 q^{5} - 32 q^{6} - 11 q^{7} - q^{9} - 22 q^{10} - 33 q^{11} + 11 q^{12} - 18 q^{13} - 33 q^{14} - 44 q^{15} - 378 q^{16} - 45 q^{18} - 22 q^{19} - 66 q^{20} - 55 q^{21} - 51 q^{23} - 58 q^{24} + 181 q^{25} + 12 q^{26} - 9 q^{27} - 44 q^{28} - 90 q^{29} - 55 q^{30} - 18 q^{31} - 11 q^{33} - 22 q^{34} - 30 q^{35} - 96 q^{36} - 22 q^{37} - 33 q^{38} + 25 q^{39} + 11 q^{40} - 66 q^{41} - 22 q^{42} - 22 q^{43} - 66 q^{44} - 30 q^{46} - 12 q^{48} + 45 q^{49} - 48 q^{50} - 11 q^{51} + 17 q^{52} - 73 q^{54} - 52 q^{55} - 231 q^{56} - 44 q^{57} + q^{58} - 11 q^{60} - 22 q^{61} + 33 q^{63} + 256 q^{64} + 22 q^{66} - 22 q^{67} - 48 q^{69} + 8 q^{70} + 223 q^{72} - 18 q^{73} - 33 q^{74} - 285 q^{75} - 22 q^{76} + 87 q^{77} - 6 q^{78} - 22 q^{79} - 165 q^{81} - 14 q^{82} - 66 q^{83} + 44 q^{84} - 28 q^{85} - 33 q^{86} - 159 q^{87} + 99 q^{88} - 66 q^{90} - 24 q^{92} + 94 q^{93} + 78 q^{94} - 61 q^{96} - 22 q^{97} - 114 q^{98} - 308 q^{99} + O(q^{100}) \)

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.