Space of modular forms of level 588 and weight 3

• 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 - 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

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 available 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

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