# Properties

 Label 588.6 Level 588 Weight 6 Dimension 19652 Nonzero newspaces 16 Sturm bound 112896 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$588 = 2^{2} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ = $$6$$ Nonzero newspaces: $$16$$ Sturm bound: $$112896$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(\Gamma_1(588))$$.

Total New Old
Modular forms 47640 19848 27792
Cusp forms 46440 19652 26788
Eisenstein series 1200 196 1004

## Trace form

 $$19652 q - 18 q^{3} - 22 q^{4} - 132 q^{5} + 15 q^{6} - 232 q^{7} + 1068 q^{8} - 1032 q^{9} + O(q^{10})$$ $$19652 q - 18 q^{3} - 22 q^{4} - 132 q^{5} + 15 q^{6} - 232 q^{7} + 1068 q^{8} - 1032 q^{9} - 3506 q^{10} + 1068 q^{11} + 2559 q^{12} + 1496 q^{13} + 3720 q^{14} - 1836 q^{15} - 2254 q^{16} - 6504 q^{17} - 8349 q^{18} - 3008 q^{19} - 1029 q^{21} + 44490 q^{22} - 7656 q^{23} - 10113 q^{24} + 9792 q^{25} - 35940 q^{26} + 2916 q^{27} - 33684 q^{28} + 65880 q^{29} - 1773 q^{30} - 13592 q^{31} + 45060 q^{32} - 40356 q^{33} + 67318 q^{34} - 36966 q^{35} + 15333 q^{36} + 108376 q^{37} - 82476 q^{38} - 42303 q^{39} + 16294 q^{40} - 70020 q^{41} - 77433 q^{42} + 27908 q^{43} - 29040 q^{44} + 14970 q^{45} + 80430 q^{46} + 40848 q^{47} + 207114 q^{48} + 380502 q^{49} + 52500 q^{50} + 152586 q^{51} - 52682 q^{52} - 84996 q^{53} - 276093 q^{54} - 276150 q^{55} - 45378 q^{56} - 100188 q^{57} - 513530 q^{58} - 400212 q^{59} - 311445 q^{60} - 76494 q^{61} + 137280 q^{63} + 438278 q^{64} + 394836 q^{65} + 567363 q^{66} + 485112 q^{67} + 661032 q^{68} + 10542 q^{69} + 223554 q^{70} + 185472 q^{71} - 473049 q^{72} - 390568 q^{73} + 72732 q^{74} - 341316 q^{75} - 517554 q^{76} - 192024 q^{77} - 512535 q^{78} - 237480 q^{79} - 2714382 q^{80} - 1172916 q^{81} - 900224 q^{82} + 461520 q^{83} + 1771254 q^{84} + 1442516 q^{85} + 2713050 q^{86} + 1600320 q^{87} + 2578920 q^{88} + 448464 q^{89} + 215178 q^{90} - 126748 q^{91} - 719334 q^{92} - 1753140 q^{93} - 2118096 q^{94} - 2454972 q^{95} - 2563158 q^{96} - 92224 q^{97} - 4208862 q^{98} - 855420 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(\Gamma_1(588))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
588.6.a $$\chi_{588}(1, \cdot)$$ 588.6.a.a 1 1
588.6.a.b 1
588.6.a.c 1
588.6.a.d 1
588.6.a.e 1
588.6.a.f 1
588.6.a.g 2
588.6.a.h 2
588.6.a.i 2
588.6.a.j 2
588.6.a.k 2
588.6.a.l 2
588.6.a.m 4
588.6.a.n 4
588.6.a.o 4
588.6.a.p 4
588.6.b $$\chi_{588}(391, \cdot)$$ n/a 200 1
588.6.e $$\chi_{588}(491, \cdot)$$ n/a 400 1
588.6.f $$\chi_{588}(293, \cdot)$$ 588.6.f.a 2 1
588.6.f.b 24
588.6.f.c 40
588.6.i $$\chi_{588}(361, \cdot)$$ 588.6.i.a 2 2
588.6.i.b 2
588.6.i.c 2
588.6.i.d 2
588.6.i.e 2
588.6.i.f 2
588.6.i.g 2
588.6.i.h 4
588.6.i.i 4
588.6.i.j 4
588.6.i.k 4
588.6.i.l 4
588.6.i.m 4
588.6.i.n 4
588.6.i.o 8
588.6.i.p 8
588.6.i.q 8
588.6.k $$\chi_{588}(509, \cdot)$$ n/a 134 2
588.6.n $$\chi_{588}(263, \cdot)$$ n/a 784 2
588.6.o $$\chi_{588}(19, \cdot)$$ n/a 400 2
588.6.q $$\chi_{588}(85, \cdot)$$ n/a 276 6
588.6.t $$\chi_{588}(41, \cdot)$$ n/a 564 6
588.6.u $$\chi_{588}(71, \cdot)$$ n/a 3336 6
588.6.x $$\chi_{588}(55, \cdot)$$ n/a 1680 6
588.6.y $$\chi_{588}(25, \cdot)$$ n/a 564 12
588.6.ba $$\chi_{588}(103, \cdot)$$ n/a 3360 12
588.6.bb $$\chi_{588}(11, \cdot)$$ n/a 6672 12
588.6.be $$\chi_{588}(5, \cdot)$$ n/a 1116 12

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

## Decomposition of $$S_{6}^{\mathrm{old}}(\Gamma_1(588))$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(\Gamma_1(588)) \cong$$ $$S_{6}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 9}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 12}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(12))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(42))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(84))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(294))$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(\Gamma_1(588))$$$$^{\oplus 1}$$