Space of modular forms of level 306 and weight 2

• Label: 306.2
• Level: 306
• Weight: 2
• Dimension: 680
• Nonzero newspaces: 10
• Newform subspaces: 47
• Sturm bound: 10368
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 10 \)
Newform subspaces:			\( 47 \)
Sturm bound:			\(10368\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(306))\).

	Total	New	Old
Modular forms	2848	680	2168
Cusp forms	2337	680	1657
Eisenstein series	511	0	511

Trace form

680 * q + 2 * q^2 + 6 * q^3 + 2 * q^4 - 6 * q^6 + 4 * q^7 - 4 * q^8 - 6 * q^9 + 4 * q^10 + 10 * q^11 + 20 * q^13 + 20 * q^14 + 6 * q^16 + 22 * q^17 + 12 * q^18 + 20 * q^19 + 4 * q^20 - 12 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 26 * q^25 - 4 * q^26 - 8 * q^28 + 32 * q^29 + 24 * q^31 + 2 * q^32 + 18 * q^33 - 3 * q^34 + 32 * q^35 - 6 * q^36 + 48 * q^37 - 26 * q^38 - 64 * q^39 - 106 * q^41 - 96 * q^42 - 74 * q^43 - 84 * q^44 - 128 * q^45 - 72 * q^46 - 252 * q^47 - 6 * q^48 - 198 * q^49 - 178 * q^50 - 137 * q^51 - 92 * q^52 - 236 * q^53 - 130 * q^54 - 176 * q^55 + 4 * q^56 - 166 * q^57 - 84 * q^58 - 170 * q^59 - 64 * q^60 - 64 * q^61 - 128 * q^62 - 72 * q^63 - 4 * q^64 - 92 * q^65 - 16 * q^66 + 26 * q^67 + q^68 + 32 * q^70 + 96 * q^71 - 6 * q^72 + 40 * q^73 + 28 * q^74 + 30 * q^75 - 2 * q^76 + 68 * q^77 + 12 * q^78 + 72 * q^79 + 16 * q^80 + 18 * q^81 + 32 * q^82 + 64 * q^83 + 12 * q^84 + 4 * q^85 + 30 * q^86 - 132 * q^87 + 26 * q^88 - 120 * q^89 - 112 * q^91 + 4 * q^92 - 128 * q^93 + 52 * q^94 - 176 * q^95 - 22 * q^97 + 48 * q^98 - 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(306))\)

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
306.2.a	\(\chi_{306}(1, \cdot)\)	306.2.a.a	1	1
		306.2.a.b	1
		306.2.a.c	1
		306.2.a.d	1
		306.2.a.e	2
		306.2.a.f	2
306.2.b	\(\chi_{306}(271, \cdot)\)	306.2.b.a	2	1
		306.2.b.b	2
		306.2.b.c	2
		306.2.b.d	2
306.2.e	\(\chi_{306}(103, \cdot)\)	306.2.e.a	2	2
		306.2.e.b	4
		306.2.e.c	6
		306.2.e.d	6
		306.2.e.e	6
		306.2.e.f	8
306.2.g	\(\chi_{306}(55, \cdot)\)	306.2.g.a	2	2
		306.2.g.b	2
		306.2.g.c	2
		306.2.g.d	2
		306.2.g.e	2
		306.2.g.f	2
		306.2.g.g	4
306.2.j	\(\chi_{306}(67, \cdot)\)	306.2.j.a	4	2
		306.2.j.b	16
		306.2.j.c	16
306.2.l	\(\chi_{306}(19, \cdot)\)	306.2.l.a	4	4
		306.2.l.b	4
		306.2.l.c	4
		306.2.l.d	8
		306.2.l.e	8
306.2.n	\(\chi_{306}(13, \cdot)\)	306.2.n.a	4	4
		306.2.n.b	4
		306.2.n.c	4
		306.2.n.d	4
		306.2.n.e	24
		306.2.n.f	32
306.2.o	\(\chi_{306}(71, \cdot)\)	306.2.o.a	8	8
		306.2.o.b	8
		306.2.o.c	8
		306.2.o.d	8
		306.2.o.e	8
		306.2.o.f	8
306.2.r	\(\chi_{306}(25, \cdot)\)	306.2.r.a	64	8
		306.2.r.b	80
306.2.s	\(\chi_{306}(5, \cdot)\)	306.2.s.a	144	16
		306.2.s.b	144

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(306))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(306)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 2}\)