↑

Properties

Label 1502.2.k
Level $1502$
Weight $2$
Character orbit 1502.k
Rep. character $\chi_{1502}(61,\cdot)$
Character field $\Q(\zeta_{75})$
Dimension $2480$
Sturm bound $376$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1502 = 2 \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1502.k (of order \(75\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{75})\)
Sturm bound: \(376\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1502, [\chi])\).

Total New Old
Modular forms 7600 2480 5120
Cusp forms 7440 2480 4960
Eisenstein series 160 0 160

Trace form

\( 2480 q + 10 q^{3} + 10 q^{9} + O(q^{10}) \) \( 2480 q + 10 q^{3} + 10 q^{9} + 10 q^{11} - 40 q^{13} - 60 q^{15} - 40 q^{21} - 20 q^{23} + 10 q^{25} - 20 q^{27} - 20 q^{28} + 30 q^{30} + 120 q^{31} + 70 q^{33} + 20 q^{34} + 20 q^{36} + 30 q^{37} + 200 q^{39} - 20 q^{40} - 20 q^{41} - 30 q^{42} - 40 q^{44} - 120 q^{45} + 20 q^{47} - 80 q^{50} - 60 q^{53} + 10 q^{55} - 120 q^{57} + 20 q^{58} - 20 q^{59} + 70 q^{60} - 210 q^{63} + 60 q^{65} + 40 q^{66} - 180 q^{67} - 90 q^{69} + 10 q^{70} - 270 q^{71} - 170 q^{73} - 110 q^{74} - 50 q^{77} + 260 q^{79} - 40 q^{80} + 70 q^{81} - 40 q^{82} - 100 q^{83} - 40 q^{84} - 290 q^{85} + 40 q^{86} - 20 q^{87} - 20 q^{88} - 110 q^{89} + 40 q^{90} - 10 q^{91} - 60 q^{92} + 220 q^{93} + 10 q^{94} + 50 q^{95} + 140 q^{97} - 120 q^{98} - 860 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1502, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1502, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1502, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(751, [\chi])\)\(^{\oplus 2}\)