↑

Properties

Label 1003.2.l
Level $1003$
Weight $2$
Character orbit 1003.l
Rep. character $\chi_{1003}(16,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $2464$
Sturm bound $180$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1003 = 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1003.l (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{58})\)
Sturm bound: \(180\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1003, [\chi])\).

Total New Old
Modular forms 2576 2576 0
Cusp forms 2464 2464 0
Eisenstein series 112 112 0

Trace form

\( 2464 q - 56 q^{2} - 140 q^{4} - 52 q^{8} + 42 q^{9} + O(q^{10}) \) \( 2464 q - 56 q^{2} - 140 q^{4} - 52 q^{8} + 42 q^{9} - 46 q^{13} - 60 q^{15} - 144 q^{16} - 32 q^{17} - 76 q^{18} - 62 q^{19} - 72 q^{21} + 26 q^{25} - 50 q^{26} - 38 q^{30} - 44 q^{32} - 62 q^{33} - 9 q^{34} - 80 q^{35} + 64 q^{36} - 78 q^{38} - 78 q^{42} - 42 q^{43} + 4 q^{47} + 134 q^{49} - 184 q^{50} + 75 q^{51} - 266 q^{52} - 20 q^{53} - 74 q^{55} - 46 q^{59} - 764 q^{60} + 352 q^{64} + 284 q^{66} - 100 q^{67} + 107 q^{68} - 298 q^{69} - 10 q^{70} - 68 q^{72} - 18 q^{76} - 58 q^{77} - 194 q^{81} - 62 q^{83} - 178 q^{84} - 13 q^{85} - 82 q^{86} + 44 q^{87} - 34 q^{89} - 86 q^{93} + 54 q^{94} - 48 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1003, [\chi])\) into newform subspaces

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