Space of modular forms of level 588 and weight 4

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

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 + 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

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 available 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

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