Space of modular forms of level 614 and weight 2

• Label: 614.2
• Level: 614
• Weight: 2
• Dimension: 3926
• Nonzero newspaces: 6
• Newform subspaces: 18
• Sturm bound: 47124
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 614 = 2 \cdot 307 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(47124\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(614))\).

	Total	New	Old
Modular forms	12087	3926	8161
Cusp forms	11476	3926	7550
Eisenstein series	611	0	611

Trace form

3926 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 - 6 * q^10 - 12 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 - 24 * q^15 - q^16 - 18 * q^17 - 13 * q^18 - 20 * q^19 - 6 * q^20 - 32 * q^21 - 12 * q^22 - 24 * q^23 - 4 * q^24 - 31 * q^25 - 14 * q^26 - 40 * q^27 - 8 * q^28 - 30 * q^29 - 24 * q^30 - 32 * q^31 - q^32 - 48 * q^33 - 18 * q^34 - 48 * q^35 - 13 * q^36 - 38 * q^37 - 20 * q^38 - 56 * q^39 - 6 * q^40 - 42 * q^41 - 32 * q^42 - 44 * q^43 - 12 * q^44 - 78 * q^45 - 24 * q^46 - 48 * q^47 - 4 * q^48 - 57 * q^49 - 31 * q^50 - 72 * q^51 - 14 * q^52 - 54 * q^53 - 40 * q^54 - 72 * q^55 - 8 * q^56 - 80 * q^57 - 30 * q^58 - 60 * q^59 - 24 * q^60 - 62 * q^61 - 32 * q^62 - 104 * q^63 - q^64 - 84 * q^65 - 48 * q^66 - 68 * q^67 - 18 * q^68 - 96 * q^69 - 48 * q^70 - 72 * q^71 - 13 * q^72 - 74 * q^73 - 38 * q^74 - 124 * q^75 - 20 * q^76 - 96 * q^77 - 56 * q^78 - 80 * q^79 - 6 * q^80 - 121 * q^81 - 42 * q^82 - 84 * q^83 - 32 * q^84 - 108 * q^85 - 44 * q^86 - 120 * q^87 - 12 * q^88 - 90 * q^89 - 78 * q^90 - 112 * q^91 - 24 * q^92 - 128 * q^93 - 48 * q^94 - 120 * q^95 - 4 * q^96 - 98 * q^97 - 57 * q^98 - 156 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(614))\)

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
614.2.a	\(\chi_{614}(1, \cdot)\)	614.2.a.a	1	1
		614.2.a.b	1
		614.2.a.c	3
		614.2.a.d	4
		614.2.a.e	6
		614.2.a.f	11
614.2.c	\(\chi_{614}(17, \cdot)\)	614.2.c.a	2	2
		614.2.c.b	4
		614.2.c.c	22
		614.2.c.d	26
614.2.e	\(\chi_{614}(53, \cdot)\)	614.2.e.a	72	6
		614.2.e.b	78
614.2.f	\(\chi_{614}(9, \cdot)\)	614.2.f.a	208	16
		614.2.f.b	224
614.2.i	\(\chi_{614}(19, \cdot)\)	614.2.i.a	416	32
		614.2.i.b	448
614.2.k	\(\chi_{614}(7, \cdot)\)	614.2.k.a	1152	96
		614.2.k.b	1248

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(614))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(614)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(307))\)\(^{\oplus 2}\)