↑

Properties

Label 1575.4.db
Level $1575$
Weight $4$
Character orbit 1575.db
Rep. character $\chi_{1575}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $5728$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1575.db (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

\( 5728 q + 5 q^{2} - 5 q^{3} - 2845 q^{4} - 8 q^{5} - 28 q^{6} - 40 q^{8} - 3 q^{9} + O(q^{10}) \) \( 5728 q + 5 q^{2} - 5 q^{3} - 2845 q^{4} - 8 q^{5} - 28 q^{6} - 40 q^{8} - 3 q^{9} - 24 q^{10} - 6 q^{11} - 5 q^{12} - 10 q^{13} - 51 q^{14} - 437 q^{15} + 11283 q^{16} - 10 q^{17} - 6 q^{19} + 128 q^{20} + 180 q^{21} - 10 q^{22} - 10 q^{23} - 286 q^{24} - 8 q^{25} + 2496 q^{26} - 680 q^{27} + 300 q^{28} - 6 q^{29} - 745 q^{30} + 3 q^{31} - 805 q^{33} + 10 q^{34} + 326 q^{35} + 470 q^{36} - 10 q^{37} - 10 q^{38} + 697 q^{39} - 482 q^{40} - 1318 q^{41} - 1090 q^{42} + 266 q^{44} - 1092 q^{45} - 38 q^{46} + 5 q^{47} - 60 q^{48} - 8 q^{49} - 908 q^{50} - 488 q^{51} + 150 q^{52} - 10 q^{53} + 29 q^{54} - 394 q^{55} + 802 q^{56} - 10 q^{58} + 2835 q^{59} + 3213 q^{60} + 3 q^{61} - 4960 q^{62} - 4625 q^{63} + 88344 q^{64} - 986 q^{65} + 25 q^{66} + 5 q^{67} + 858 q^{69} + 2028 q^{70} + 2748 q^{71} - 645 q^{72} - 10 q^{73} + 48 q^{74} - 5578 q^{75} - 176 q^{76} + 1415 q^{77} + 250 q^{78} + 255 q^{79} + 4534 q^{80} - 2479 q^{81} + 130 q^{83} - 435 q^{84} + 117 q^{85} + 5458 q^{86} - 5 q^{87} - 10 q^{88} + 6306 q^{89} - 12348 q^{90} - 2070 q^{91} + 3110 q^{92} + 67 q^{94} + 3138 q^{95} - 1637 q^{96} - 10 q^{97} - 60 q^{98} + 2610 q^{99} + O(q^{100}) \)

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.