Space of modular forms of level 608 and weight 3

• Label: 608.3
• Level: 608
• Weight: 3
• Dimension: 12718
• Nonzero newspaces: 18
• Sturm bound: 69120
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(69120\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(608))\).

	Total	New	Old
Modular forms	23616	13058	10558
Cusp forms	22464	12718	9746
Eisenstein series	1152	340	812

Trace form

12718 * q - 64 * q^2 - 50 * q^3 - 64 * q^4 - 72 * q^5 - 64 * q^6 - 46 * q^7 - 64 * q^8 - 62 * q^9 + 16 * q^10 - 18 * q^11 + 32 * q^12 - 8 * q^13 - 32 * q^14 - 38 * q^15 - 104 * q^16 - 112 * q^17 - 184 * q^18 - 84 * q^19 - 296 * q^20 - 192 * q^21 - 360 * q^22 + 82 * q^23 - 488 * q^24 - 66 * q^25 - 264 * q^26 + 202 * q^27 - 184 * q^28 - 8 * q^29 - 112 * q^30 - 54 * q^31 - 24 * q^32 - 172 * q^33 + 24 * q^34 - 238 * q^35 + 600 * q^36 + 56 * q^37 + 324 * q^38 - 484 * q^39 + 744 * q^40 + 48 * q^41 + 776 * q^42 - 210 * q^43 + 304 * q^44 + 64 * q^45 - 38 * q^47 - 168 * q^48 - 74 * q^49 - 688 * q^50 - 510 * q^51 - 912 * q^52 - 8 * q^53 - 1256 * q^54 - 558 * q^55 - 1176 * q^56 - 268 * q^57 - 1200 * q^58 - 466 * q^59 - 952 * q^60 - 264 * q^61 - 504 * q^62 - 54 * q^63 + 392 * q^64 - 52 * q^65 + 1088 * q^66 + 398 * q^67 + 664 * q^68 + 192 * q^69 + 1256 * q^70 + 466 * q^71 + 1424 * q^72 - 80 * q^73 + 992 * q^74 + 840 * q^75 + 444 * q^76 - 456 * q^77 + 400 * q^78 + 986 * q^79 - 696 * q^80 + 366 * q^81 - 1344 * q^82 + 1230 * q^83 - 2056 * q^84 - 408 * q^85 - 1448 * q^86 + 850 * q^87 - 1416 * q^88 - 272 * q^89 - 1816 * q^90 + 338 * q^91 - 1304 * q^92 - 648 * q^93 - 152 * q^94 - 54 * q^95 + 112 * q^96 + 80 * q^97 + 584 * q^98 - 626 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(608))\)

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
608.3.d	\(\chi_{608}(191, \cdot)\)	608.3.d.a	16	1
		608.3.d.b	20
608.3.e	\(\chi_{608}(417, \cdot)\)	608.3.e.a	20	1
		608.3.e.b	20
608.3.f	\(\chi_{608}(495, \cdot)\)	608.3.f.a	36	1
608.3.g	\(\chi_{608}(113, \cdot)\)	608.3.g.a	3	1
		608.3.g.b	3
		608.3.g.c	32
608.3.j	\(\chi_{608}(265, \cdot)\)	None	0	2
608.3.l	\(\chi_{608}(39, \cdot)\)	None	0	2
608.3.o	\(\chi_{608}(239, \cdot)\)	608.3.o.a	4	2
		608.3.o.b	72
608.3.p	\(\chi_{608}(145, \cdot)\)	608.3.p.a	76	2
608.3.q	\(\chi_{608}(159, \cdot)\)	608.3.q.a	40	2
		608.3.q.b	40
608.3.r	\(\chi_{608}(65, \cdot)\)	608.3.r.a	40	2
		608.3.r.b	40
608.3.w	\(\chi_{608}(37, \cdot)\)	n/a	632	4
608.3.x	\(\chi_{608}(115, \cdot)\)	n/a	576	4
608.3.ba	\(\chi_{608}(217, \cdot)\)	None	0	4
608.3.bc	\(\chi_{608}(7, \cdot)\)	None	0	4
608.3.bd	\(\chi_{608}(33, \cdot)\)	n/a	240	6
608.3.be	\(\chi_{608}(241, \cdot)\)	n/a	228	6
608.3.bg	\(\chi_{608}(47, \cdot)\)	n/a	228	6
608.3.bj	\(\chi_{608}(63, \cdot)\)	n/a	240	6
608.3.bk	\(\chi_{608}(11, \cdot)\)	n/a	1264	8
608.3.bl	\(\chi_{608}(69, \cdot)\)	n/a	1264	8
608.3.bp	\(\chi_{608}(23, \cdot)\)	None	0	12
608.3.br	\(\chi_{608}(41, \cdot)\)	None	0	12
608.3.bu	\(\chi_{608}(35, \cdot)\)	n/a	3792	24
608.3.bv	\(\chi_{608}(13, \cdot)\)	n/a	3792	24

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(608))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(608)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)