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Properties

Label 1503.2.i
Level $1503$
Weight $2$
Character orbit 1503.i
Rep. character $\chi_{1503}(19,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $5658$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1503 = 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1503.i (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1503, [\chi])\).

Total New Old
Modular forms 14104 5822 8282
Cusp forms 13448 5658 7790
Eisenstein series 656 164 492

Trace form

\( 5658 q + 81 q^{2} - 153 q^{4} + 79 q^{5} - 81 q^{7} + 71 q^{8} + O(q^{10}) \) \( 5658 q + 81 q^{2} - 153 q^{4} + 79 q^{5} - 81 q^{7} + 71 q^{8} - 87 q^{10} + 83 q^{11} - 81 q^{13} + 89 q^{14} - 155 q^{16} + 79 q^{17} - 87 q^{19} + 67 q^{20} - 71 q^{22} + 77 q^{23} - 146 q^{25} + 73 q^{26} - 75 q^{28} + 75 q^{29} - 99 q^{31} + 57 q^{32} - 85 q^{34} + 57 q^{35} - 75 q^{37} + 83 q^{38} - 89 q^{40} + 81 q^{41} - 87 q^{43} + 68 q^{44} - 67 q^{46} + 111 q^{47} - 112 q^{49} + 71 q^{50} - 81 q^{52} + 85 q^{53} - 101 q^{55} + 81 q^{56} - 61 q^{58} + 85 q^{59} - 79 q^{61} + 74 q^{62} - 117 q^{64} + 101 q^{65} - 87 q^{67} + 119 q^{68} - 51 q^{70} + 99 q^{71} - 91 q^{73} + 79 q^{74} - 87 q^{76} + 59 q^{77} - 53 q^{79} + 57 q^{80} - 97 q^{82} + 101 q^{83} - 101 q^{85} + 71 q^{86} - 43 q^{88} + 63 q^{89} - 21 q^{91} + 39 q^{92} - 93 q^{94} + 63 q^{95} - 85 q^{97} + 100 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1503, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1503, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1503, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 2}\)