Properties

Label 2475.4.cy
Level $2475$
Weight $4$
Character orbit 2475.cy
Rep. character $\chi_{2475}(301,\cdot)$
Character field $\Q(\zeta_{15})$
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.cy (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
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 8736 5520 3216
Cusp forms 8544 5424 3120
Eisenstein series 192 96 96

Trace form

\( 5424 q + 7 q^{2} + 2 q^{3} + 2691 q^{4} + 28 q^{6} + 3 q^{7} - 52 q^{8} - 44 q^{9} + O(q^{10}) \) \( 5424 q + 7 q^{2} + 2 q^{3} + 2691 q^{4} + 28 q^{6} + 3 q^{7} - 52 q^{8} - 44 q^{9} + 17 q^{11} + 262 q^{12} + 3 q^{13} - 93 q^{14} + 10535 q^{16} - 488 q^{17} - 142 q^{18} - 258 q^{19} + 158 q^{21} + 2 q^{22} - 540 q^{23} + 522 q^{24} - 308 q^{26} - 328 q^{27} + 300 q^{28} + 251 q^{29} + 9 q^{31} - 1880 q^{32} + 967 q^{33} + 236 q^{34} - 2842 q^{36} + 84 q^{37} - 127 q^{38} - 562 q^{39} - 15 q^{41} + 1197 q^{42} + 350 q^{43} + 1954 q^{44} - 84 q^{46} - 793 q^{47} + 944 q^{48} + 31461 q^{49} - 1135 q^{51} + 243 q^{52} + 736 q^{53} - 1358 q^{54} + 1822 q^{56} - 3198 q^{57} + 791 q^{58} + 234 q^{59} - 9 q^{61} + 4502 q^{62} + 1190 q^{63} - 80996 q^{64} - 6181 q^{66} + 2006 q^{67} + 4824 q^{68} - 269 q^{69} + 2480 q^{71} - 3839 q^{72} + 2496 q^{73} - 1409 q^{74} - 688 q^{76} + 3290 q^{77} + 7624 q^{78} + 1191 q^{79} + 5856 q^{81} + 3176 q^{82} + 3103 q^{83} + 14961 q^{84} - 2459 q^{86} + 922 q^{87} + 3572 q^{88} + 11912 q^{89} + 2848 q^{91} + 7959 q^{92} - 2270 q^{93} - 1749 q^{94} - 4419 q^{96} - 654 q^{97} + 15720 q^{98} - 7373 q^{99} + O(q^{100}) \)

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

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