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Properties

Label 2475.4.i
Level $2475$
Weight $4$
Character orbit 2475.i
Rep. character $\chi_{2475}(826,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $1140$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 2184 1140 1044
Cusp forms 2136 1140 996
Eisenstein series 48 0 48

Trace form

\( 1140 q - 2 q^{3} - 2280 q^{4} + 46 q^{6} + 12 q^{7} - 12 q^{8} + 44 q^{9} + O(q^{10}) \) \( 1140 q - 2 q^{3} - 2280 q^{4} + 46 q^{6} + 12 q^{7} - 12 q^{8} + 44 q^{9} - 44 q^{11} + 234 q^{12} - 24 q^{13} - 250 q^{14} - 9120 q^{16} - 96 q^{17} + 204 q^{18} + 120 q^{19} - 80 q^{21} + 288 q^{23} - 62 q^{24} + 1944 q^{26} - 308 q^{27} - 384 q^{28} - 84 q^{29} + 138 q^{31} - 472 q^{32} - 176 q^{33} - 396 q^{34} - 2614 q^{36} + 408 q^{37} + 1370 q^{38} + 304 q^{39} - 156 q^{41} + 2046 q^{42} - 168 q^{43} + 880 q^{44} - 1080 q^{46} + 800 q^{47} + 2138 q^{48} - 27774 q^{49} + 1460 q^{51} - 1302 q^{52} - 908 q^{53} - 496 q^{54} - 3300 q^{56} - 4192 q^{57} - 594 q^{58} - 210 q^{59} + 804 q^{61} + 636 q^{62} + 2712 q^{63} + 72132 q^{64} - 550 q^{66} + 282 q^{67} + 3014 q^{68} - 30 q^{69} + 8004 q^{71} - 3924 q^{72} - 672 q^{73} - 3094 q^{74} + 156 q^{76} + 616 q^{77} - 10150 q^{78} - 420 q^{79} - 2964 q^{81} + 2340 q^{82} + 572 q^{83} + 6682 q^{84} - 224 q^{86} + 7952 q^{87} - 496 q^{89} + 3480 q^{91} + 4762 q^{92} + 6232 q^{93} + 126 q^{94} + 4160 q^{96} - 1896 q^{97} + 5660 q^{98} - 330 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{4}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)