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Properties

Label 1449.2.bw
Level $1449$
Weight $2$
Character orbit 1449.bw
Rep. character $\chi_{1449}(25,\cdot)$
Character field $\Q(\zeta_{33})$
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.bw (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1449 \)
Character field: \(\Q(\zeta_{33})\)
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

\( 3760 q - 18 q^{2} - 9 q^{3} - 386 q^{4} + q^{5} - 40 q^{6} - 9 q^{7} - 64 q^{8} - 17 q^{9} + O(q^{10}) \) \( 3760 q - 18 q^{2} - 9 q^{3} - 386 q^{4} + q^{5} - 40 q^{6} - 9 q^{7} - 64 q^{8} - 17 q^{9} - 10 q^{10} + 9 q^{11} + 19 q^{12} - 18 q^{13} + 11 q^{14} - 14 q^{15} - 362 q^{16} - 34 q^{17} + 27 q^{18} - 18 q^{19} - 30 q^{20} - 21 q^{21} - 32 q^{22} + 11 q^{23} - 14 q^{24} + 181 q^{25} - 30 q^{26} - 63 q^{27} - 24 q^{28} - 30 q^{29} + 3 q^{30} - 18 q^{31} + 30 q^{32} - 49 q^{33} - 22 q^{34} - 26 q^{35} - 88 q^{36} - 18 q^{37} - 27 q^{38} + 25 q^{39} + 23 q^{40} - 10 q^{41} + 34 q^{42} - 18 q^{43} + 16 q^{44} - 28 q^{45} - 22 q^{46} - 16 q^{47} - 32 q^{48} - 63 q^{49} - 12 q^{50} + q^{51} + 33 q^{52} - 18 q^{53} - 65 q^{54} - 52 q^{55} - 53 q^{56} - 46 q^{57} + 17 q^{58} + 2 q^{59} + 43 q^{60} + 6 q^{61} - 64 q^{62} + 65 q^{63} - 368 q^{64} - 232 q^{65} - 40 q^{66} - 18 q^{67} + 524 q^{68} - 50 q^{69} - 88 q^{70} - 40 q^{71} + 207 q^{72} - 18 q^{73} + 33 q^{74} - 285 q^{75} - 18 q^{76} - 179 q^{77} - 170 q^{78} - 18 q^{79} - 22 q^{80} + 51 q^{81} - 22 q^{82} - 38 q^{83} - 6 q^{84} - 28 q^{85} - 19 q^{86} + 237 q^{87} - 71 q^{88} - 94 q^{89} - 56 q^{90} - 108 q^{91} - 52 q^{92} + 22 q^{93} - 210 q^{94} - 58 q^{95} - 221 q^{96} - 18 q^{97} - 62 q^{98} + 208 q^{99} + O(q^{100}) \)

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.