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Properties

Label 1502.2.h
Level $1502$
Weight $2$
Character orbit 1502.h
Rep. character $\chi_{1502}(51,\cdot)$
Character field $\Q(\zeta_{25})$
Dimension $1280$
Sturm bound $376$

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Defining parameters

Level: \( N \) \(=\) \( 1502 = 2 \cdot 751 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1502.h (of order \(25\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 751 \)
Character field: \(\Q(\zeta_{25})\)
Sturm bound: \(376\)

Dimensions

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

Total New Old
Modular forms 3800 1280 2520
Cusp forms 3720 1280 2440
Eisenstein series 80 0 80

Trace form

\( 1280 q - 10 q^{3} - 10 q^{9} + O(q^{10}) \) \( 1280 q - 10 q^{3} - 10 q^{9} - 10 q^{11} + 80 q^{13} + 60 q^{15} - 20 q^{21} - 10 q^{23} - 10 q^{25} - 10 q^{27} - 10 q^{28} - 30 q^{30} + 160 q^{31} - 70 q^{33} - 20 q^{34} - 20 q^{36} - 40 q^{37} + 40 q^{39} - 10 q^{40} - 100 q^{41} + 30 q^{42} - 20 q^{44} - 60 q^{45} - 20 q^{47} - 10 q^{48} + 80 q^{50} + 60 q^{53} - 10 q^{55} + 100 q^{57} - 20 q^{58} - 10 q^{59} + 20 q^{60} + 90 q^{63} - 120 q^{65} - 40 q^{66} + 150 q^{67} - 60 q^{69} - 10 q^{70} + 270 q^{71} - 100 q^{73} + 50 q^{74} + 50 q^{77} + 40 q^{79} - 20 q^{80} - 190 q^{81} - 20 q^{82} + 100 q^{83} - 50 q^{84} - 10 q^{85} - 40 q^{86} - 100 q^{87} - 10 q^{88} - 10 q^{89} - 40 q^{90} - 50 q^{91} + 60 q^{92} - 200 q^{93} - 70 q^{94} - 50 q^{95} + 70 q^{97} + 60 q^{98} + 410 q^{99} + O(q^{100}) \)

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

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