Space of modular forms of level 306 and weight 4

• Label: 306.4
• Level: 306
• Weight: 4
• Dimension: 2038
• Nonzero newspaces: 10
• Sturm bound: 20736
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 306 = 2 \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 10 \)
Sturm bound:			\(20736\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(306))\).

	Total	New	Old
Modular forms	8032	2038	5994
Cusp forms	7520	2038	5482
Eisenstein series	512	0	512

Trace form

2038 * q - 8 * q^2 - 6 * q^3 + 16 * q^4 - 24 * q^5 + 36 * q^6 + 8 * q^7 + 16 * q^8 + 210 * q^9 + 128 * q^10 + 170 * q^11 - 48 * q^12 - 92 * q^13 - 296 * q^14 - 180 * q^15 - 304 * q^17 - 312 * q^18 - 620 * q^19 - 112 * q^20 + 72 * q^21 + 308 * q^22 + 1280 * q^23 + 48 * q^24 + 2292 * q^25 + 928 * q^26 + 320 * q^28 + 496 * q^29 + 576 * q^30 - 676 * q^31 - 128 * q^32 - 1530 * q^33 - 342 * q^34 - 3848 * q^35 - 1032 * q^36 - 1564 * q^37 - 3268 * q^38 - 4084 * q^39 + 96 * q^40 - 4802 * q^41 - 480 * q^42 + 638 * q^43 + 1488 * q^44 + 3964 * q^45 + 2544 * q^46 + 10248 * q^47 + 288 * q^48 + 10560 * q^49 + 7528 * q^50 + 6553 * q^51 + 4496 * q^52 + 8360 * q^53 + 2348 * q^54 + 9848 * q^55 - 544 * q^56 - 694 * q^57 - 960 * q^58 - 4810 * q^59 - 688 * q^60 - 6800 * q^61 - 8128 * q^62 - 6588 * q^63 - 896 * q^64 - 15976 * q^65 - 3616 * q^66 - 6014 * q^67 + 92 * q^68 - 2988 * q^69 + 3216 * q^70 + 4464 * q^71 + 48 * q^72 + 3772 * q^73 - 1792 * q^74 - 6462 * q^75 + 680 * q^76 - 3224 * q^77 - 264 * q^78 + 1588 * q^79 + 320 * q^80 - 630 * q^81 + 696 * q^82 - 7660 * q^83 - 1488 * q^84 - 22876 * q^85 - 2244 * q^86 - 4056 * q^87 - 1968 * q^88 - 3204 * q^89 + 864 * q^90 - 9560 * q^91 + 3008 * q^92 + 8980 * q^93 - 1224 * q^94 + 20096 * q^95 - 768 * q^96 + 8018 * q^97 - 1332 * q^98 + 11376 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(306))\)

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
306.4.a	\(\chi_{306}(1, \cdot)\)	306.4.a.a	1	1
		306.4.a.b	1
		306.4.a.c	1
		306.4.a.d	1
		306.4.a.e	1
		306.4.a.f	1
		306.4.a.g	1
		306.4.a.h	1
		306.4.a.i	2
		306.4.a.j	2
		306.4.a.k	2
		306.4.a.l	3
		306.4.a.m	3
306.4.b	\(\chi_{306}(271, \cdot)\)	306.4.b.a	2	1
		306.4.b.b	2
		306.4.b.c	4
		306.4.b.d	4
		306.4.b.e	4
		306.4.b.f	6
306.4.e	\(\chi_{306}(103, \cdot)\)	306.4.e.a	4	2
		306.4.e.b	18
		306.4.e.c	22
		306.4.e.d	26
		306.4.e.e	26
306.4.g	\(\chi_{306}(55, \cdot)\)	306.4.g.a	2	2
		306.4.g.b	4
		306.4.g.c	4
		306.4.g.d	6
		306.4.g.e	8
		306.4.g.f	8
		306.4.g.g	12
306.4.j	\(\chi_{306}(67, \cdot)\)	n/a	108	2
306.4.l	\(\chi_{306}(19, \cdot)\)	306.4.l.a	8	4
		306.4.l.b	12
		306.4.l.c	16
		306.4.l.d	16
		306.4.l.e	20
		306.4.l.f	20
306.4.n	\(\chi_{306}(13, \cdot)\)	n/a	216	4
306.4.o	\(\chi_{306}(71, \cdot)\)	n/a	144	8
306.4.r	\(\chi_{306}(25, \cdot)\)	n/a	432	8
306.4.s	\(\chi_{306}(5, \cdot)\)	n/a	864	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(306))\) into lower level spaces

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