Properties

Label 588.4
Level 588
Weight 4
Dimension 11753
Nonzero newspaces 16
Sturm bound 75264
Trace bound 5

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Defining parameters

Level: \( N \) = \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(75264\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(588))\).

Total New Old
Modular forms 28824 11949 16875
Cusp forms 27624 11753 15871
Eisenstein series 1200 196 1004

Trace form

\( 11753 q - 9 q^{3} - 38 q^{4} + 30 q^{5} - 33 q^{6} + 48 q^{7} + 204 q^{8} + 51 q^{9} + O(q^{10}) \) \( 11753 q - 9 q^{3} - 38 q^{4} + 30 q^{5} - 33 q^{6} + 48 q^{7} + 204 q^{8} + 51 q^{9} + 14 q^{10} - 300 q^{11} - 225 q^{12} - 542 q^{13} - 312 q^{14} - 198 q^{15} - 590 q^{16} - 6 q^{17} - 45 q^{18} + 668 q^{19} + 252 q^{21} + 714 q^{22} - 96 q^{23} + 975 q^{24} - 1865 q^{25} + 1500 q^{26} - 81 q^{27} + 1260 q^{28} - 2538 q^{29} + 51 q^{30} + 32 q^{31} + 420 q^{32} - 78 q^{33} - 778 q^{34} + 960 q^{35} + 117 q^{36} + 7090 q^{37} - 2988 q^{38} + 3540 q^{39} - 1210 q^{40} + 378 q^{41} + 687 q^{42} - 964 q^{43} - 3696 q^{44} - 948 q^{45} - 2802 q^{46} - 3792 q^{47} - 630 q^{48} - 6108 q^{49} + 2100 q^{50} - 2970 q^{51} + 5462 q^{52} - 90 q^{53} + 1827 q^{54} + 1620 q^{55} + 5022 q^{56} + 1494 q^{57} + 8678 q^{58} + 5004 q^{59} + 3003 q^{60} + 2122 q^{61} - 1446 q^{63} - 5690 q^{64} - 6204 q^{65} - 5085 q^{66} - 8068 q^{67} - 14904 q^{68} - 7866 q^{69} - 9966 q^{70} - 1368 q^{71} - 3081 q^{72} - 698 q^{73} - 6468 q^{74} + 3393 q^{75} - 1746 q^{76} - 756 q^{77} - 5319 q^{78} + 5552 q^{79} - 14382 q^{80} - 441 q^{81} - 12256 q^{82} - 6876 q^{83} - 17946 q^{84} + 6760 q^{85} + 2394 q^{86} + 8562 q^{87} + 5544 q^{88} + 4674 q^{89} + 6762 q^{90} + 7848 q^{91} + 4410 q^{92} + 11970 q^{93} + 7536 q^{94} + 23808 q^{95} + 22986 q^{96} + 3538 q^{97} + 45906 q^{98} - 3300 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(588))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
588.4.a \(\chi_{588}(1, \cdot)\) 588.4.a.a 1 1
588.4.a.b 1
588.4.a.c 1
588.4.a.d 1
588.4.a.e 1
588.4.a.f 2
588.4.a.g 2
588.4.a.h 2
588.4.a.i 2
588.4.a.j 4
588.4.a.k 4
588.4.b \(\chi_{588}(391, \cdot)\) n/a 120 1
588.4.e \(\chi_{588}(491, \cdot)\) n/a 236 1
588.4.f \(\chi_{588}(293, \cdot)\) 588.4.f.a 2 1
588.4.f.b 2
588.4.f.c 12
588.4.f.d 24
588.4.i \(\chi_{588}(361, \cdot)\) 588.4.i.a 2 2
588.4.i.b 2
588.4.i.c 2
588.4.i.d 2
588.4.i.e 2
588.4.i.f 2
588.4.i.g 2
588.4.i.h 2
588.4.i.i 4
588.4.i.j 4
588.4.i.k 8
588.4.i.l 8
588.4.k \(\chi_{588}(509, \cdot)\) 588.4.k.a 2 2
588.4.k.b 2
588.4.k.c 12
588.4.k.d 16
588.4.k.e 48
588.4.n \(\chi_{588}(263, \cdot)\) n/a 464 2
588.4.o \(\chi_{588}(19, \cdot)\) n/a 240 2
588.4.q \(\chi_{588}(85, \cdot)\) n/a 168 6
588.4.t \(\chi_{588}(41, \cdot)\) n/a 336 6
588.4.u \(\chi_{588}(71, \cdot)\) n/a 1992 6
588.4.x \(\chi_{588}(55, \cdot)\) n/a 1008 6
588.4.y \(\chi_{588}(25, \cdot)\) n/a 336 12
588.4.ba \(\chi_{588}(103, \cdot)\) n/a 2016 12
588.4.bb \(\chi_{588}(11, \cdot)\) n/a 3984 12
588.4.be \(\chi_{588}(5, \cdot)\) n/a 672 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(588))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(588)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)