Space of modular forms of level 608 and weight 4

• Label: 608.4
• Level: 608
• Weight: 4
• Dimension: 19162
• Nonzero newspaces: 18
• Sturm bound: 92160
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(92160\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(608))\).

	Total	New	Old
Modular forms	35136	19502	15634
Cusp forms	33984	19162	14822
Eisenstein series	1152	340	812

Trace form

19162 * q - 64 * q^2 - 46 * q^3 - 64 * q^4 - 68 * q^5 - 64 * q^6 - 78 * q^7 - 64 * q^8 - 190 * q^9 - 304 * q^10 - 46 * q^11 + 32 * q^12 + 172 * q^13 + 352 * q^14 + 170 * q^15 + 536 * q^16 + 328 * q^17 + 296 * q^18 - 50 * q^19 - 296 * q^20 - 576 * q^21 - 456 * q^22 - 1310 * q^23 + 24 * q^24 - 770 * q^25 - 104 * q^26 + 482 * q^27 - 824 * q^28 + 332 * q^29 - 2448 * q^30 + 2346 * q^31 - 1304 * q^32 + 780 * q^33 - 1128 * q^34 + 866 * q^35 - 2984 * q^36 - 1732 * q^37 - 1052 * q^38 - 2420 * q^39 + 1000 * q^40 - 1000 * q^41 + 4456 * q^42 - 1662 * q^43 + 4016 * q^44 + 2388 * q^45 + 2816 * q^46 + 1290 * q^47 + 4824 * q^48 + 2114 * q^49 + 7056 * q^50 + 2714 * q^51 + 4976 * q^52 - 964 * q^53 + 2104 * q^54 - 142 * q^55 - 2456 * q^56 - 1136 * q^57 - 6544 * q^58 - 2798 * q^59 - 11576 * q^60 + 1804 * q^61 - 6840 * q^62 - 5046 * q^63 - 9976 * q^64 - 3612 * q^65 - 12064 * q^66 - 4126 * q^67 - 5608 * q^68 + 512 * q^69 - 2872 * q^70 - 782 * q^71 + 3344 * q^72 + 1400 * q^73 + 6880 * q^74 + 3352 * q^75 + 5052 * q^76 - 1384 * q^77 + 23760 * q^78 - 1910 * q^79 + 20552 * q^80 + 2962 * q^81 + 12736 * q^82 - 4926 * q^83 + 13048 * q^84 + 1872 * q^85 + 1784 * q^86 + 5890 * q^87 - 2568 * q^88 + 3480 * q^89 - 14872 * q^90 + 7154 * q^91 - 20376 * q^92 - 10088 * q^93 - 25752 * q^94 + 5250 * q^95 - 35728 * q^96 - 4888 * q^97 - 22520 * q^98 + 10794 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(608))\)

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
608.4.a	\(\chi_{608}(1, \cdot)\)	608.4.a.a	1	1
		608.4.a.b	1
		608.4.a.c	2
		608.4.a.d	2
		608.4.a.e	5
		608.4.a.f	5
		608.4.a.g	5
		608.4.a.h	5
		608.4.a.i	7
		608.4.a.j	7
		608.4.a.k	7
		608.4.a.l	7
608.4.b	\(\chi_{608}(303, \cdot)\)	608.4.b.a	2	1
		608.4.b.b	56
608.4.c	\(\chi_{608}(305, \cdot)\)	608.4.c.a	54	1
608.4.h	\(\chi_{608}(607, \cdot)\)	608.4.h.a	60	1
608.4.i	\(\chi_{608}(353, \cdot)\)	n/a	120	2
608.4.k	\(\chi_{608}(153, \cdot)\)	None	0	2
608.4.m	\(\chi_{608}(151, \cdot)\)	None	0	2
608.4.n	\(\chi_{608}(31, \cdot)\)	n/a	120	2
608.4.s	\(\chi_{608}(335, \cdot)\)	n/a	116	2
608.4.t	\(\chi_{608}(49, \cdot)\)	n/a	116	2
608.4.u	\(\chi_{608}(75, \cdot)\)	n/a	952	4
608.4.v	\(\chi_{608}(77, \cdot)\)	n/a	864	4
608.4.y	\(\chi_{608}(161, \cdot)\)	n/a	360	6
608.4.z	\(\chi_{608}(121, \cdot)\)	None	0	4
608.4.bb	\(\chi_{608}(103, \cdot)\)	None	0	4
608.4.bf	\(\chi_{608}(17, \cdot)\)	n/a	348	6
608.4.bh	\(\chi_{608}(15, \cdot)\)	n/a	348	6
608.4.bi	\(\chi_{608}(127, \cdot)\)	n/a	360	6
608.4.bm	\(\chi_{608}(45, \cdot)\)	n/a	1904	8
608.4.bn	\(\chi_{608}(27, \cdot)\)	n/a	1904	8
608.4.bo	\(\chi_{608}(71, \cdot)\)	None	0	12
608.4.bq	\(\chi_{608}(9, \cdot)\)	None	0	12
608.4.bs	\(\chi_{608}(5, \cdot)\)	n/a	5712	24
608.4.bt	\(\chi_{608}(3, \cdot)\)	n/a	5712	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(608))\) into lower level spaces

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