Properties

Label 570.4.k
Level $570$
Weight $4$
Character orbit 570.k
Rep. character $\chi_{570}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $216$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(570, [\chi])\).

Total New Old
Modular forms 736 216 520
Cusp forms 704 216 488
Eisenstein series 32 0 32

Trace form

\( 216 q - 16 q^{3} - 16 q^{6} - 24 q^{7} + O(q^{10}) \) \( 216 q - 16 q^{3} - 16 q^{6} - 24 q^{7} - 48 q^{10} + 64 q^{12} + 48 q^{13} + 8 q^{15} - 3456 q^{16} - 928 q^{21} - 336 q^{22} - 1152 q^{25} + 848 q^{27} - 96 q^{28} - 336 q^{30} + 432 q^{31} - 1984 q^{33} - 736 q^{36} - 1104 q^{37} + 384 q^{40} + 528 q^{42} + 1344 q^{43} + 2304 q^{46} + 256 q^{48} + 1680 q^{51} - 192 q^{52} - 2040 q^{55} - 4560 q^{58} - 1088 q^{60} - 240 q^{61} - 5792 q^{63} + 2880 q^{67} + 3216 q^{70} - 72 q^{73} - 4352 q^{75} + 2480 q^{78} + 5272 q^{81} - 4416 q^{82} + 2160 q^{85} - 1344 q^{88} - 3984 q^{90} - 6528 q^{91} - 2888 q^{93} + 256 q^{96} + 12888 q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(570, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(570, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)