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Properties

Label 3003.2.hw
Level $3003$
Weight $2$
Character orbit 3003.hw
Rep. character $\chi_{3003}(269,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $3520$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 3003 = 3 \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3003.hw (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3003 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3003, [\chi])\).

Total New Old
Modular forms 3648 3648 0
Cusp forms 3520 3520 0
Eisenstein series 128 128 0

Trace form

\( 3520 q - 9 q^{3} + 852 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{9} + O(q^{10}) \) \( 3520 q - 9 q^{3} + 852 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{9} - 48 q^{10} - 60 q^{12} - 18 q^{15} - 860 q^{16} - 22 q^{18} - 18 q^{19} - 54 q^{21} + 21 q^{24} + 396 q^{25} + 38 q^{28} - 51 q^{30} - 36 q^{31} - 120 q^{33} - 12 q^{36} - 12 q^{37} + 15 q^{39} - 180 q^{40} - 19 q^{42} - 32 q^{43} + 84 q^{46} - 24 q^{48} + 2 q^{49} + 38 q^{51} + 30 q^{52} + 18 q^{55} - 36 q^{57} - 22 q^{58} - 2 q^{60} - 18 q^{61} + 13 q^{63} + 848 q^{64} - 75 q^{66} + 80 q^{67} - 18 q^{69} - 38 q^{70} - 9 q^{72} - 36 q^{73} + 72 q^{76} - 70 q^{78} - 44 q^{79} + 17 q^{81} - 90 q^{82} - 121 q^{84} - 56 q^{85} + 44 q^{88} + 128 q^{91} + 82 q^{93} + 90 q^{94} + 150 q^{96} + 48 q^{97} - 62 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3003, [\chi])\) into newform subspaces

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