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Properties

Label 1575.4.dq
Level $1575$
Weight $4$
Character orbit 1575.dq
Rep. character $\chi_{1575}(104,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $5728$
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.dq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1575 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 5792 5792 0
Cusp forms 5728 5728 0
Eisenstein series 64 64 0

Trace form

\( 5728 q - 30 q^{2} + 2842 q^{4} - 12 q^{9} + O(q^{10}) \) \( 5728 q - 30 q^{2} + 2842 q^{4} - 12 q^{9} - 18 q^{11} - 9 q^{14} + 306 q^{15} + 11290 q^{16} + 27 q^{21} - 10 q^{22} - 30 q^{23} - 8 q^{25} - 660 q^{28} - 18 q^{29} + 316 q^{30} + 110 q^{36} - 40 q^{37} - 292 q^{39} + 1070 q^{42} - 88 q^{46} - 8 q^{49} - 1824 q^{50} + 928 q^{51} - 3144 q^{56} - 10 q^{58} + 7376 q^{60} - 3175 q^{63} - 88504 q^{64} + 1284 q^{65} - 10 q^{67} - 1474 q^{70} - 660 q^{72} - 144 q^{74} + 8145 q^{77} - 560 q^{78} + 498 q^{79} + 412 q^{81} - 4505 q^{84} - 258 q^{85} - 8358 q^{86} - 10 q^{88} + 2046 q^{91} - 9390 q^{92} + 4818 q^{95} + 4068 q^{99} + O(q^{100}) \)

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.