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Properties

Label 1449.2.cp
Level $1449$
Weight $2$
Character orbit 1449.cp
Rep. character $\chi_{1449}(61,\cdot)$
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.cp (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

\( 3760 q + 9 q^{2} - 27 q^{3} + 193 q^{4} - 12 q^{6} - 11 q^{7} - 64 q^{8} - 5 q^{9} + O(q^{10}) \) \( 3760 q + 9 q^{2} - 27 q^{3} + 193 q^{4} - 12 q^{6} - 11 q^{7} - 64 q^{8} - 5 q^{9} - 66 q^{10} - 22 q^{11} - 27 q^{12} - 11 q^{14} - 44 q^{15} + 181 q^{16} - 66 q^{17} + 47 q^{18} - 66 q^{19} - 55 q^{21} - 6 q^{23} - 78 q^{24} - 362 q^{25} - 18 q^{26} - 81 q^{27} - 44 q^{28} - 6 q^{29} - 99 q^{30} - 27 q^{31} - 15 q^{32} - 33 q^{33} - 26 q^{35} - 8 q^{36} - 22 q^{37} - 13 q^{39} + 24 q^{41} - 22 q^{42} - 22 q^{43} - 44 q^{44} - 10 q^{46} - 24 q^{47} + 12 q^{48} + 99 q^{49} - 28 q^{50} - 11 q^{51} - 22 q^{53} + 9 q^{54} + 121 q^{56} - 44 q^{57} - 34 q^{58} + 3 q^{59} - 11 q^{60} - 33 q^{61} - 132 q^{63} - 368 q^{64} - 66 q^{65} - 33 q^{66} + 11 q^{67} + 30 q^{69} + 14 q^{70} - 104 q^{71} + 143 q^{72} - 54 q^{73} - 22 q^{74} + 3 q^{75} + 23 q^{77} + 50 q^{78} + 11 q^{79} - 66 q^{80} + 143 q^{81} - 42 q^{82} - 154 q^{84} - 28 q^{85} - 110 q^{86} - 339 q^{87} - 198 q^{88} - 66 q^{89} - 66 q^{90} - 76 q^{92} - 90 q^{93} - 27 q^{94} - 3 q^{95} + 3 q^{96} - 98 q^{98} - 308 q^{99} + O(q^{100}) \)

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.