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Properties

Label 1575.4.eg
Level $1575$
Weight $4$
Character orbit 1575.eg
Rep. character $\chi_{1575}(13,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $11456$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.eg (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1575, [\chi])\).

Total New Old
Modular forms 11584 11584 0
Cusp forms 11456 11456 0
Eisenstein series 128 128 0

Trace form

\( 11456 q - 16 q^{2} - 20 q^{4} - 8 q^{7} - 40 q^{9} + O(q^{10}) \) \( 11456 q - 16 q^{2} - 20 q^{4} - 8 q^{7} - 40 q^{9} - 12 q^{11} - 10 q^{14} - 200 q^{15} - 22540 q^{16} + 16 q^{18} - 12 q^{21} - 80 q^{22} + 88 q^{23} - 16 q^{25} + 256 q^{28} - 20 q^{29} + 376 q^{30} + 124 q^{32} - 1112 q^{35} + 488 q^{36} - 64 q^{37} + 2400 q^{39} + 1298 q^{42} - 16 q^{43} - 80 q^{44} - 48 q^{46} + 776 q^{50} - 64 q^{51} - 2304 q^{53} + 506 q^{56} + 704 q^{57} - 960 q^{58} - 12320 q^{60} + 1214 q^{63} - 80 q^{64} + 680 q^{65} - 16 q^{67} - 508 q^{70} - 48 q^{71} - 2348 q^{72} - 4660 q^{77} + 4732 q^{78} - 20 q^{79} - 24 q^{81} - 1940 q^{84} - 16 q^{85} - 12 q^{86} + 2512 q^{88} - 24 q^{91} + 1776 q^{92} + 5212 q^{93} + 1380 q^{95} + 232 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1575, [\chi])\) into newform subspaces

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