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Properties

Label 2475.4.ez
Level $2475$
Weight $4$
Character orbit 2475.ez
Rep. character $\chi_{2475}(101,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $5424$
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.ez (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 8736 5520 3216
Cusp forms 8544 5424 3120
Eisenstein series 192 96 96

Trace form

\( 5424 q + 15 q^{2} + 10 q^{3} + 2691 q^{4} - 80 q^{6} + 5 q^{7} + 148 q^{9} + O(q^{10}) \) \( 5424 q + 15 q^{2} + 10 q^{3} + 2691 q^{4} - 80 q^{6} + 5 q^{7} + 148 q^{9} + 51 q^{11} - 90 q^{12} + 5 q^{13} + 9 q^{14} + 10535 q^{16} + 470 q^{18} + 470 q^{19} + 38 q^{22} + 276 q^{23} + 490 q^{24} - 320 q^{27} + 20 q^{28} - 885 q^{29} - 27 q^{31} - 935 q^{33} - 124 q^{34} + 206 q^{36} - 60 q^{37} + 1671 q^{38} + 2000 q^{39} - 45 q^{41} + 2931 q^{42} + 20 q^{46} + 1173 q^{47} - 2924 q^{48} - 31455 q^{49} + 1215 q^{51} + 5 q^{52} + 1866 q^{56} + 3900 q^{57} - 721 q^{58} - 3684 q^{59} - 15 q^{61} - 3940 q^{63} - 80996 q^{64} - 4773 q^{66} - 442 q^{67} - 11490 q^{68} + 2245 q^{69} + 5095 q^{72} + 20 q^{73} + 15 q^{74} - 5244 q^{77} - 2848 q^{78} + 5 q^{79} + 1040 q^{81} + 3176 q^{82} - 6375 q^{83} + 15635 q^{84} - 8013 q^{86} - 4348 q^{88} + 104 q^{91} + 633 q^{92} - 58 q^{93} + 5 q^{94} - 14895 q^{96} - 492 q^{97} - 2989 q^{99} + O(q^{100}) \)

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

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