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Properties

Label 2007.2.z
Level $2007$
Weight $2$
Character orbit 2007.z
Rep. character $\chi_{2007}(31,\cdot)$
Character field $\Q(\zeta_{111})$
Dimension $15984$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 2007 = 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2007.z (of order \(111\) and degree \(72\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2007 \)
Character field: \(\Q(\zeta_{111})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2007, [\chi])\).

Total New Old
Modular forms 16272 16272 0
Cusp forms 15984 15984 0
Eisenstein series 288 288 0

Trace form

\( 15984 q - 35 q^{2} - 72 q^{3} + 185 q^{4} - 31 q^{5} - 63 q^{6} - 37 q^{7} - 142 q^{8} - 80 q^{9} + O(q^{10}) \) \( 15984 q - 35 q^{2} - 72 q^{3} + 185 q^{4} - 31 q^{5} - 63 q^{6} - 37 q^{7} - 142 q^{8} - 80 q^{9} - 148 q^{10} - 48 q^{11} + 29 q^{12} - 34 q^{13} - 45 q^{14} - 66 q^{15} + 185 q^{16} - 134 q^{17} + 14 q^{18} - 145 q^{19} - 43 q^{20} - 78 q^{21} - 43 q^{22} - 48 q^{23} + 113 q^{24} - 475 q^{25} - 84 q^{26} - 63 q^{27} - 148 q^{28} - 238 q^{29} - 52 q^{30} - 28 q^{31} - 41 q^{32} - 66 q^{33} - 31 q^{34} - 167 q^{35} - 5 q^{36} - 142 q^{37} + 25 q^{38} - 64 q^{39} - 62 q^{40} - 23 q^{41} - 69 q^{42} - 19 q^{43} - 175 q^{44} - 71 q^{45} - 154 q^{46} - 480 q^{47} - 74 q^{48} + 167 q^{49} + 2 q^{50} - 92 q^{51} - 52 q^{52} - 156 q^{53} - 107 q^{54} - 124 q^{55} - 11 q^{56} + 20 q^{57} - 37 q^{58} - 58 q^{59} - 117 q^{60} - 37 q^{61} - 348 q^{62} - 75 q^{63} - 562 q^{64} - 30 q^{65} - 54 q^{66} - 55 q^{67} - 34 q^{68} - 73 q^{69} - 37 q^{70} - 157 q^{71} + 54 q^{72} - 139 q^{73} - 103 q^{74} + 127 q^{75} - 34 q^{76} - 31 q^{77} - 124 q^{78} - 244 q^{79} - 264 q^{80} - 124 q^{81} - 184 q^{82} - 41 q^{83} - 117 q^{84} - 13 q^{85} - 12 q^{86} - 1098 q^{87} - 40 q^{88} - 180 q^{89} - 1391 q^{90} - 178 q^{91} - 15 q^{92} - 74 q^{93} - 13 q^{94} - 88 q^{95} + 540 q^{96} - 40 q^{97} + 1210 q^{98} - 114 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2007, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.