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Properties

Label 2475.4.cx
Level $2475$
Weight $4$
Character orbit 2475.cx
Rep. character $\chi_{2475}(421,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $8608$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2475.cx (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2475 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2475, [\chi])\).

Total New Old
Modular forms 8672 8672 0
Cusp forms 8608 8608 0
Eisenstein series 64 64 0

Trace form

\( 8608 q - q^{2} - 8 q^{3} + 4287 q^{4} + q^{5} + 36 q^{6} - 6 q^{7} + 12 q^{8} + 46 q^{9} + O(q^{10}) \) \( 8608 q - q^{2} - 8 q^{3} + 4287 q^{4} + q^{5} + 36 q^{6} - 6 q^{7} + 12 q^{8} + 46 q^{9} - 64 q^{10} - 3 q^{11} - 208 q^{12} - q^{13} - 70 q^{14} + 4 q^{15} + 17015 q^{16} - 24 q^{17} - 44 q^{18} - 4 q^{19} - 499 q^{20} - 120 q^{21} - 35 q^{22} - 238 q^{23} + 236 q^{24} - 75 q^{25} - 88 q^{26} - 890 q^{27} - 420 q^{28} + 695 q^{29} + 1398 q^{30} + 53 q^{31} + 176 q^{32} - 1221 q^{33} - 14 q^{34} + 8 q^{35} + 1364 q^{36} + 552 q^{37} + 3 q^{38} + 165 q^{39} - 282 q^{40} + 1311 q^{41} - 2048 q^{42} - 16 q^{43} - 220 q^{44} + 900 q^{45} - 88 q^{46} + 775 q^{47} - 3950 q^{48} + 51542 q^{49} - 179 q^{50} - 66 q^{51} + 794 q^{52} + 2896 q^{53} - 596 q^{54} - 878 q^{55} + 1486 q^{56} + 540 q^{57} + 1023 q^{58} + 326 q^{59} - 189 q^{60} - q^{61} + 6272 q^{62} - 819 q^{63} - 134004 q^{64} + 440 q^{65} - 2432 q^{66} - 924 q^{67} - 134 q^{68} - 1615 q^{69} - 194 q^{70} - 1864 q^{71} + 3541 q^{72} - 4 q^{73} + 2946 q^{74} - 4174 q^{75} + 176 q^{76} + 1329 q^{77} + 3576 q^{78} + 750 q^{79} + 2776 q^{80} + 1310 q^{81} - 8 q^{82} + 2814 q^{83} + 3270 q^{84} - 1003 q^{85} + 15 q^{86} + 3528 q^{87} + 309 q^{88} + 1016 q^{89} - 946 q^{90} + 682 q^{91} - 10581 q^{92} - 6459 q^{93} + 3402 q^{94} + 2134 q^{95} + 4100 q^{96} + 1146 q^{97} + 598 q^{98} - 250 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

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