Space of modular forms of level 608 and weight 2

• Label: 608.2
• Level: 608
• Weight: 2
• Dimension: 6274
• Nonzero newspaces: 18
• Newform subspaces: 41
• Sturm bound: 46080
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 608 = 2^{5} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 41 \)
Sturm bound:			\(46080\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(608))\).

	Total	New	Old
Modular forms	12096	6614	5482
Cusp forms	10945	6274	4671
Eisenstein series	1151	340	811

Trace form

6274 * q - 64 * q^2 - 46 * q^3 - 64 * q^4 - 60 * q^5 - 64 * q^6 - 46 * q^7 - 64 * q^8 - 94 * q^9 - 80 * q^10 - 46 * q^11 - 96 * q^12 - 76 * q^13 - 96 * q^14 - 54 * q^15 - 104 * q^16 - 40 * q^17 - 104 * q^18 - 50 * q^19 - 168 * q^20 - 64 * q^21 - 88 * q^22 - 62 * q^23 - 40 * q^24 - 98 * q^25 - 24 * q^26 - 94 * q^27 - 24 * q^28 - 44 * q^29 - 86 * q^31 - 24 * q^32 - 164 * q^33 - 40 * q^34 - 94 * q^35 - 8 * q^36 - 60 * q^37 - 76 * q^38 - 148 * q^39 - 88 * q^40 - 120 * q^41 - 104 * q^42 - 62 * q^43 - 144 * q^44 - 100 * q^45 - 128 * q^46 - 54 * q^47 - 168 * q^48 - 22 * q^49 - 144 * q^50 - 38 * q^51 - 80 * q^52 - 124 * q^53 - 88 * q^54 + 18 * q^55 - 88 * q^56 - 104 * q^57 - 128 * q^58 + 18 * q^59 - 56 * q^60 - 108 * q^61 - 24 * q^62 + 42 * q^63 + 8 * q^64 - 140 * q^65 - 16 * q^66 + 34 * q^67 - 104 * q^68 - 128 * q^69 - 40 * q^70 + 18 * q^71 - 112 * q^72 - 88 * q^73 - 96 * q^74 - 40 * q^75 - 68 * q^76 - 168 * q^77 - 144 * q^78 - 54 * q^79 - 56 * q^80 - 54 * q^81 - 64 * q^82 - 126 * q^83 - 104 * q^84 - 96 * q^85 - 24 * q^86 - 158 * q^87 - 72 * q^88 - 120 * q^89 - 88 * q^90 - 142 * q^91 + 8 * q^92 - 40 * q^93 - 88 * q^94 - 110 * q^95 - 144 * q^96 - 200 * q^97 - 24 * q^98 - 150 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)

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
608.2.a	\(\chi_{608}(1, \cdot)\)	608.2.a.a	1	1
		608.2.a.b	1
		608.2.a.c	1
		608.2.a.d	1
		608.2.a.e	1
		608.2.a.f	1
		608.2.a.g	2
		608.2.a.h	2
		608.2.a.i	4
		608.2.a.j	4
608.2.b	\(\chi_{608}(303, \cdot)\)	608.2.b.a	2	1
		608.2.b.b	4
		608.2.b.c	12
608.2.c	\(\chi_{608}(305, \cdot)\)	608.2.c.a	2	1
		608.2.c.b	16
608.2.h	\(\chi_{608}(607, \cdot)\)	608.2.h.a	20	1
608.2.i	\(\chi_{608}(353, \cdot)\)	608.2.i.a	2	2
		608.2.i.b	2
		608.2.i.c	8
		608.2.i.d	8
		608.2.i.e	8
		608.2.i.f	12
608.2.k	\(\chi_{608}(153, \cdot)\)	None	0	2
608.2.m	\(\chi_{608}(151, \cdot)\)	None	0	2
608.2.n	\(\chi_{608}(31, \cdot)\)	608.2.n.a	40	2
608.2.s	\(\chi_{608}(335, \cdot)\)	608.2.s.a	4	2
		608.2.s.b	4
		608.2.s.c	28
608.2.t	\(\chi_{608}(49, \cdot)\)	608.2.t.a	36	2
608.2.u	\(\chi_{608}(75, \cdot)\)	608.2.u.a	312	4
608.2.v	\(\chi_{608}(77, \cdot)\)	608.2.v.a	288	4
608.2.y	\(\chi_{608}(161, \cdot)\)	608.2.y.a	24	6
		608.2.y.b	30
		608.2.y.c	30
		608.2.y.d	36
608.2.z	\(\chi_{608}(121, \cdot)\)	None	0	4
608.2.bb	\(\chi_{608}(103, \cdot)\)	None	0	4
608.2.bf	\(\chi_{608}(17, \cdot)\)	608.2.bf.a	108	6
608.2.bh	\(\chi_{608}(15, \cdot)\)	608.2.bh.a	12	6
		608.2.bh.b	96
608.2.bi	\(\chi_{608}(127, \cdot)\)	608.2.bi.a	120	6
608.2.bm	\(\chi_{608}(45, \cdot)\)	608.2.bm.a	624	8
608.2.bn	\(\chi_{608}(27, \cdot)\)	608.2.bn.a	624	8
608.2.bo	\(\chi_{608}(71, \cdot)\)	None	0	12
608.2.bq	\(\chi_{608}(9, \cdot)\)	None	0	12
608.2.bs	\(\chi_{608}(5, \cdot)\)	608.2.bs.a	1872	24
608.2.bt	\(\chi_{608}(3, \cdot)\)	608.2.bt.a	1872	24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(608))\) into lower level spaces

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