Space of modular forms of level 588 and weight 6

• 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 - 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

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}$