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Properties

Label 1500.4.y
Level $1500$
Weight $4$
Character orbit 1500.y
Rep. character $\chi_{1500}(61,\cdot)$
Character field $\Q(\zeta_{25})$
Dimension $1520$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1500.y (of order \(25\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 125 \)
Character field: \(\Q(\zeta_{25})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1500, [\chi])\).

Total New Old
Modular forms 18120 1520 16600
Cusp forms 17880 1520 16360
Eisenstein series 240 0 240

Trace form

\( 1520 q + O(q^{10}) \) \( 1520 q - 140 q^{11} - 320 q^{17} - 60 q^{19} + 1000 q^{23} + 960 q^{25} + 80 q^{29} + 690 q^{31} - 480 q^{33} - 860 q^{35} + 370 q^{37} + 480 q^{41} - 560 q^{43} - 1720 q^{47} - 20580 q^{49} - 1020 q^{51} - 2310 q^{53} + 620 q^{55} + 1640 q^{59} + 720 q^{61} - 180 q^{63} + 650 q^{65} + 360 q^{67} - 4640 q^{71} - 840 q^{73} + 1120 q^{77} + 1080 q^{79} + 5920 q^{83} + 1650 q^{85} + 1140 q^{87} + 4230 q^{89} - 7920 q^{91} + 3420 q^{93} + 12360 q^{95} + 1710 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1500, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1500, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1500, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(125, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(250, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(375, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(500, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(750, [\chi])\)\(^{\oplus 2}\)