Space of modular forms of level 588 and weight 8

• Label: 588.8
• Level: 588
• Weight: 8
• Dimension: 27554
• Nonzero newspaces: 16
• Sturm bound: 150528
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 16 \)
Sturm bound:			\(150528\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(588))\).

	Total	New	Old
Modular forms	66456	27750	38706
Cusp forms	65256	27554	37702
Eisenstein series	1200	196	1004

Trace form

27554 * q + 54 * q^3 - 6 * q^4 - 120 * q^5 - 225 * q^6 + 664 * q^7 - 3444 * q^8 - 3438 * q^9 + 37614 * q^10 + 33132 * q^11 - 26913 * q^12 - 75228 * q^13 - 39288 * q^14 + 28332 * q^15 + 176562 * q^16 + 65148 * q^17 + 52899 * q^18 - 54576 * q^19 - 155631 * q^21 - 59766 * q^22 + 225672 * q^23 - 185937 * q^24 - 170470 * q^25 + 818940 * q^26 - 78732 * q^27 + 834540 * q^28 - 1262628 * q^29 - 1298589 * q^30 + 493152 * q^31 - 2187420 * q^32 + 2647104 * q^33 - 24138 * q^34 + 317010 * q^35 - 1305771 * q^36 - 4606796 * q^37 + 603252 * q^38 - 3064143 * q^39 - 2846970 * q^40 + 2245032 * q^41 + 1262703 * q^42 + 3137252 * q^43 + 6197136 * q^44 + 1857582 * q^45 + 6297390 * q^46 - 7132704 * q^47 - 8863350 * q^48 - 15585462 * q^49 - 9187500 * q^50 - 430398 * q^51 - 4157418 * q^52 + 7359768 * q^53 + 6664131 * q^54 + 41486250 * q^55 + 2613726 * q^56 + 936576 * q^57 - 8617242 * q^58 - 17181540 * q^59 + 5581083 * q^60 - 30350974 * q^61 + 3586152 * q^63 - 4773306 * q^64 + 3616356 * q^65 - 9236973 * q^66 - 15911720 * q^67 - 7309944 * q^68 + 10587534 * q^69 - 26908446 * q^70 - 19213776 * q^71 - 1745961 * q^72 - 2364276 * q^73 + 26472732 * q^74 + 4881708 * q^75 + 39586158 * q^76 + 36824760 * q^77 + 19676649 * q^78 + 53309680 * q^79 - 112976622 * q^80 + 50995710 * q^81 + 82068624 * q^82 + 32840928 * q^83 + 67854726 * q^84 - 65594340 * q^85 - 24184854 * q^86 - 34232424 * q^87 - 248240088 * q^88 - 44967900 * q^89 - 153733518 * q^90 - 30626252 * q^91 - 80800902 * q^92 - 17379312 * q^93 + 182254176 * q^94 + 119389668 * q^95 + 292308618 * q^96 + 205804668 * q^97 + 461139042 * q^98 + 61750020 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(588))\)

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
588.8.a	\(\chi_{588}(1, \cdot)\)	588.8.a.a	1	1
		588.8.a.b	1
		588.8.a.c	1
		588.8.a.d	1
		588.8.a.e	2
		588.8.a.f	2
		588.8.a.g	3
		588.8.a.h	3
		588.8.a.i	4
		588.8.a.j	4
		588.8.a.k	5
		588.8.a.l	5
		588.8.a.m	8
		588.8.a.n	8
588.8.b	\(\chi_{588}(391, \cdot)\)	n/a	280	1
588.8.e	\(\chi_{588}(491, \cdot)\)	n/a	564	1
588.8.f	\(\chi_{588}(293, \cdot)\)	588.8.f.a	2	1
		588.8.f.b	36
		588.8.f.c	56
588.8.i	\(\chi_{588}(361, \cdot)\)	588.8.i.a	2	2
		588.8.i.b	2
		588.8.i.c	2
		588.8.i.d	2
		588.8.i.e	2
		588.8.i.f	2
		588.8.i.g	2
		588.8.i.h	2
		588.8.i.i	4
		588.8.i.j	4
		588.8.i.k	4
		588.8.i.l	4
		588.8.i.m	6
		588.8.i.n	6
		588.8.i.o	8
		588.8.i.p	10
		588.8.i.q	16
		588.8.i.r	16
588.8.k	\(\chi_{588}(509, \cdot)\)	n/a	186	2
588.8.n	\(\chi_{588}(263, \cdot)\)	n/a	1104	2
588.8.o	\(\chi_{588}(19, \cdot)\)	n/a	560	2
588.8.q	\(\chi_{588}(85, \cdot)\)	n/a	396	6
588.8.t	\(\chi_{588}(41, \cdot)\)	n/a	780	6
588.8.u	\(\chi_{588}(71, \cdot)\)	n/a	4680	6
588.8.x	\(\chi_{588}(55, \cdot)\)	n/a	2352	6
588.8.y	\(\chi_{588}(25, \cdot)\)	n/a	780	12
588.8.ba	\(\chi_{588}(103, \cdot)\)	n/a	4704	12
588.8.bb	\(\chi_{588}(11, \cdot)\)	n/a	9360	12
588.8.be	\(\chi_{588}(5, \cdot)\)	n/a	1572	12

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(588))\) into lower level spaces

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