Space of modular forms of level 676 and weight 3

• Label: 676.3
• Level: 676
• Weight: 3
• Dimension: 16162
• Nonzero newspaces: 12
• Sturm bound: 85176
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(85176\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(676))\).

	Total	New	Old
Modular forms	28962	16572	12390
Cusp forms	27822	16162	11660
Eisenstein series	1140	410	730

Trace form

16162 * q - 66 * q^2 - 66 * q^4 - 132 * q^5 - 66 * q^6 - 20 * q^7 - 66 * q^8 - 180 * q^9 - 66 * q^10 - 12 * q^11 - 54 * q^12 - 132 * q^13 - 126 * q^14 + 72 * q^15 - 66 * q^16 - 24 * q^17 + 186 * q^18 + 256 * q^19 + 174 * q^20 + 96 * q^21 + 114 * q^22 + 48 * q^23 + 30 * q^24 - 108 * q^25 - 102 * q^26 - 144 * q^27 - 246 * q^28 - 468 * q^29 - 546 * q^30 - 340 * q^31 - 486 * q^32 - 696 * q^33 - 498 * q^34 - 420 * q^35 - 570 * q^36 - 232 * q^37 - 54 * q^38 + 72 * q^39 - 654 * q^40 + 672 * q^41 - 822 * q^42 + 396 * q^43 - 486 * q^44 + 828 * q^45 - 666 * q^46 + 420 * q^47 - 354 * q^48 + 480 * q^49 - 126 * q^50 - 18 * q^52 - 660 * q^53 + 210 * q^54 - 516 * q^55 + 474 * q^56 - 1464 * q^57 + 606 * q^58 - 372 * q^59 + 1314 * q^60 - 1104 * q^61 + 1134 * q^62 + 204 * q^63 + 1818 * q^64 - 150 * q^65 + 1914 * q^66 + 496 * q^67 + 1338 * q^68 + 864 * q^69 + 1242 * q^70 + 744 * q^71 + 714 * q^72 + 508 * q^73 + 438 * q^74 + 480 * q^75 + 54 * q^76 - 108 * q^77 - 186 * q^78 - 264 * q^79 - 750 * q^80 - 792 * q^81 - 666 * q^82 - 972 * q^83 - 1830 * q^84 - 1368 * q^85 - 2286 * q^86 - 1176 * q^87 - 2550 * q^88 - 1380 * q^89 - 4110 * q^90 - 310 * q^91 - 2718 * q^92 - 1608 * q^93 - 2154 * q^94 - 624 * q^95 - 2262 * q^96 - 76 * q^97 - 1194 * q^98 + 36 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(676))\)

We only show spaces with odd 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
676.3.b	\(\chi_{676}(675, \cdot)\)	n/a	144	1
676.3.c	\(\chi_{676}(339, \cdot)\)	n/a	144	1
676.3.g	\(\chi_{676}(437, \cdot)\)	676.3.g.a	4	2
		676.3.g.b	6
		676.3.g.c	8
		676.3.g.d	8
		676.3.g.e	24
676.3.i	\(\chi_{676}(23, \cdot)\)	n/a	288	2
676.3.j	\(\chi_{676}(191, \cdot)\)	n/a	288	2
676.3.k	\(\chi_{676}(89, \cdot)\)	n/a	104	4
676.3.o	\(\chi_{676}(27, \cdot)\)	n/a	2160	12
676.3.p	\(\chi_{676}(51, \cdot)\)	n/a	2160	12
676.3.r	\(\chi_{676}(5, \cdot)\)	n/a	744	24
676.3.t	\(\chi_{676}(3, \cdot)\)	n/a	4320	24
676.3.u	\(\chi_{676}(43, \cdot)\)	n/a	4320	24
676.3.x	\(\chi_{676}(33, \cdot)\)	n/a	1440	48

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(676))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(676)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)