# Properties

 Label 588.3 Level 588 Weight 3 Dimension 7803 Nonzero newspaces 16 Sturm bound 56448 Trace bound 3

## Defining parameters

 Level: $$N$$ = $$588 = 2^{2} \cdot 3 \cdot 7^{2}$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$16$$ Sturm bound: $$56448$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(588))$$.

Total New Old
Modular forms 19416 7995 11421
Cusp forms 18216 7803 10413
Eisenstein series 1200 192 1008

## Trace form

 $$7803 q - 2 q^{2} + 3 q^{3} - 34 q^{4} + 8 q^{5} - 15 q^{6} - 8 q^{7} - 44 q^{8} - 81 q^{9} + O(q^{10})$$ $$7803 q - 2 q^{2} + 3 q^{3} - 34 q^{4} + 8 q^{5} - 15 q^{6} - 8 q^{7} - 44 q^{8} - 81 q^{9} - 134 q^{10} - 108 q^{11} - 57 q^{12} - 130 q^{13} + 24 q^{14} - 12 q^{15} + 98 q^{16} + 116 q^{17} + 141 q^{18} + 106 q^{19} + 512 q^{20} - 63 q^{21} + 378 q^{22} - 96 q^{23} + 147 q^{24} - 113 q^{25} + 56 q^{26} + 225 q^{27} - 84 q^{28} + 260 q^{29} + 3 q^{30} + 154 q^{31} - 332 q^{32} + 384 q^{33} - 566 q^{34} + 78 q^{35} + 177 q^{36} + 30 q^{37} - 324 q^{38} - 279 q^{39} - 362 q^{40} - 472 q^{41} + 57 q^{42} - 378 q^{43} + 480 q^{44} - 378 q^{45} + 414 q^{46} - 216 q^{47} + 48 q^{48} + 66 q^{49} + 462 q^{50} - 378 q^{51} + 94 q^{52} + 200 q^{53} - 363 q^{54} + 462 q^{55} - 354 q^{56} - 534 q^{57} - 1334 q^{58} + 180 q^{59} - 1101 q^{60} + 388 q^{61} - 1488 q^{62} + 192 q^{63} - 1402 q^{64} - 140 q^{65} - 1137 q^{66} + 386 q^{67} - 952 q^{68} + 810 q^{69} - 306 q^{70} + 336 q^{71} - 1065 q^{72} + 758 q^{73} + 608 q^{74} + 1149 q^{75} + 822 q^{76} + 504 q^{77} + 429 q^{78} + 1442 q^{79} + 2750 q^{80} + 1071 q^{81} + 3712 q^{82} + 2352 q^{83} + 2970 q^{84} + 1412 q^{85} + 2958 q^{86} + 744 q^{87} + 3708 q^{88} + 860 q^{89} + 2760 q^{90} + 568 q^{91} + 990 q^{92} - 402 q^{93} + 2244 q^{94} + 12 q^{95} + 2136 q^{96} + 1406 q^{97} + 42 q^{98} - 540 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(588))$$

We only show spaces with odd 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
588.3.c $$\chi_{588}(197, \cdot)$$ 588.3.c.a 1 1
588.3.c.b 1
588.3.c.c 1
588.3.c.d 2
588.3.c.e 2
588.3.c.f 2
588.3.c.g 2
588.3.c.h 4
588.3.c.i 4
588.3.c.j 8
588.3.d $$\chi_{588}(97, \cdot)$$ 588.3.d.a 2 1
588.3.d.b 4
588.3.d.c 8
588.3.g $$\chi_{588}(295, \cdot)$$ 588.3.g.a 2 1
588.3.g.b 2
588.3.g.c 2
588.3.g.d 12
588.3.g.e 12
588.3.g.f 14
588.3.g.g 14
588.3.g.h 24
588.3.h $$\chi_{588}(587, \cdot)$$ n/a 152 1
588.3.j $$\chi_{588}(215, \cdot)$$ n/a 304 2
588.3.l $$\chi_{588}(67, \cdot)$$ n/a 160 2
588.3.m $$\chi_{588}(313, \cdot)$$ 588.3.m.a 2 2
588.3.m.b 2
588.3.m.c 2
588.3.m.d 4
588.3.m.e 8
588.3.m.f 8
588.3.p $$\chi_{588}(557, \cdot)$$ 588.3.p.a 2 2
588.3.p.b 2
588.3.p.c 2
588.3.p.d 4
588.3.p.e 4
588.3.p.f 8
588.3.p.g 8
588.3.p.h 8
588.3.p.i 16
588.3.r $$\chi_{588}(83, \cdot)$$ n/a 1320 6
588.3.s $$\chi_{588}(43, \cdot)$$ n/a 672 6
588.3.v $$\chi_{588}(13, \cdot)$$ n/a 108 6
588.3.w $$\chi_{588}(29, \cdot)$$ n/a 228 6
588.3.z $$\chi_{588}(53, \cdot)$$ n/a 444 12
588.3.bc $$\chi_{588}(61, \cdot)$$ n/a 228 12
588.3.bd $$\chi_{588}(151, \cdot)$$ n/a 1344 12
588.3.bf $$\chi_{588}(47, \cdot)$$ n/a 2640 12

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

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(588))$$ into lower level spaces

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