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Properties

Label 2475.4.o
Level $2475$
Weight $4$
Character orbit 2475.o
Rep. character $\chi_{2475}(676,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $1128$
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.o (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(1440\)

Dimensions

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

Total New Old
Modular forms 4416 1152 3264
Cusp forms 4224 1128 3096
Eisenstein series 192 24 168

Trace form

\( 1128 q - 3 q^{2} - 1103 q^{4} - 17 q^{7} + 95 q^{8} + O(q^{10}) \) \( 1128 q - 3 q^{2} - 1103 q^{4} - 17 q^{7} + 95 q^{8} + 33 q^{11} - 59 q^{13} - 132 q^{14} - 4623 q^{16} + 69 q^{17} + 170 q^{19} - 251 q^{22} + 268 q^{23} - 406 q^{26} - 128 q^{28} - 559 q^{29} - 691 q^{31} - 1808 q^{32} - 66 q^{34} + 375 q^{37} + 1140 q^{38} - 299 q^{41} - 178 q^{43} + 5356 q^{44} + 2336 q^{46} + 685 q^{47} - 12771 q^{49} - 1664 q^{52} - 245 q^{53} - 28 q^{56} - 1582 q^{58} - 724 q^{59} - 375 q^{61} + 1912 q^{62} - 17759 q^{64} + 4294 q^{67} + 148 q^{68} - 741 q^{71} - 3805 q^{73} - 276 q^{74} - 1966 q^{76} - 1095 q^{77} + 1733 q^{79} - 3787 q^{82} - 1198 q^{83} + 8021 q^{86} - 1183 q^{88} + 522 q^{89} - 267 q^{91} - 1252 q^{92} + 1258 q^{94} - 2070 q^{97} - 2888 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)