Space of modular forms of level 425 and weight 6

• Label: 425.6
• Level: 425
• Weight: 6
• Dimension: 32642
• Nonzero newspaces: 20
• Sturm bound: 86400
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(86400\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(425))\).

	Total	New	Old
Modular forms	36448	33256	3192
Cusp forms	35552	32642	2910
Eisenstein series	896	614	282

Trace form

32642 * q - 76 * q^2 - 100 * q^3 - 292 * q^4 - 238 * q^5 + 892 * q^6 + 684 * q^7 - 564 * q^8 - 2216 * q^9 - 888 * q^10 + 1924 * q^11 + 4588 * q^12 + 1868 * q^13 + 3916 * q^14 + 2332 * q^15 - 6604 * q^16 - 3452 * q^17 - 22172 * q^18 - 14596 * q^19 - 20628 * q^20 - 2292 * q^21 + 27148 * q^22 + 33868 * q^23 + 69680 * q^24 + 37902 * q^25 + 35888 * q^26 + 33680 * q^27 - 24900 * q^28 - 91624 * q^29 - 107788 * q^30 - 23068 * q^31 - 88572 * q^32 - 47332 * q^33 - 32122 * q^34 + 80504 * q^35 + 92396 * q^36 + 66686 * q^37 + 130984 * q^38 - 25428 * q^39 - 179608 * q^40 - 39904 * q^41 - 211948 * q^42 - 66620 * q^43 - 33240 * q^44 + 35442 * q^45 - 113836 * q^46 + 43604 * q^47 + 410456 * q^48 + 330038 * q^49 + 504772 * q^50 + 144 * q^51 + 82856 * q^52 - 25230 * q^53 - 220728 * q^54 - 182388 * q^55 - 104628 * q^56 - 268068 * q^57 - 259928 * q^58 - 71872 * q^59 - 195108 * q^60 + 197796 * q^61 - 71120 * q^62 - 302472 * q^63 - 488520 * q^64 - 272458 * q^65 - 697692 * q^66 - 136572 * q^67 + 1040570 * q^68 + 977016 * q^69 + 511140 * q^70 + 223804 * q^71 - 900192 * q^72 - 1498880 * q^73 - 1195120 * q^74 - 151540 * q^75 - 1071912 * q^76 + 189884 * q^77 + 836368 * q^78 + 796732 * q^79 + 897012 * q^80 + 1490008 * q^81 + 3328868 * q^82 + 408984 * q^83 + 1724148 * q^84 + 657139 * q^85 - 556436 * q^86 - 198720 * q^87 - 47268 * q^88 - 359978 * q^89 - 1597076 * q^90 - 464812 * q^91 - 981084 * q^92 - 547688 * q^93 - 2713236 * q^94 - 536980 * q^95 - 4863828 * q^96 - 834260 * q^97 - 609420 * q^98 - 763320 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(425))\)

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
425.6.a	\(\chi_{425}(1, \cdot)\)	425.6.a.a	1	1
		425.6.a.b	1
		425.6.a.c	4
		425.6.a.d	5
		425.6.a.e	7
		425.6.a.f	8
		425.6.a.g	8
		425.6.a.h	11
		425.6.a.i	11
		425.6.a.j	15
		425.6.a.k	15
		425.6.a.l	20
		425.6.a.m	20
425.6.b	\(\chi_{425}(324, \cdot)\)	n/a	120	1
425.6.c	\(\chi_{425}(424, \cdot)\)	n/a	132	1
425.6.d	\(\chi_{425}(101, \cdot)\)	n/a	140	1
425.6.e	\(\chi_{425}(251, \cdot)\)	n/a	280	2
425.6.j	\(\chi_{425}(149, \cdot)\)	n/a	264	2
425.6.k	\(\chi_{425}(86, \cdot)\)	n/a	800	4
425.6.m	\(\chi_{425}(26, \cdot)\)	n/a	556	4
425.6.n	\(\chi_{425}(49, \cdot)\)	n/a	536	4
425.6.p	\(\chi_{425}(16, \cdot)\)	n/a	888	4
425.6.q	\(\chi_{425}(84, \cdot)\)	n/a	896	4
425.6.r	\(\chi_{425}(69, \cdot)\)	n/a	800	4
425.6.s	\(\chi_{425}(7, \cdot)\)	n/a	1064	8
425.6.v	\(\chi_{425}(82, \cdot)\)	n/a	1064	8
425.6.w	\(\chi_{425}(4, \cdot)\)	n/a	1792	8
425.6.bb	\(\chi_{425}(21, \cdot)\)	n/a	1776	8
425.6.bd	\(\chi_{425}(9, \cdot)\)	n/a	3552	16
425.6.be	\(\chi_{425}(36, \cdot)\)	n/a	3584	16
425.6.bg	\(\chi_{425}(12, \cdot)\)	n/a	7136	32
425.6.bj	\(\chi_{425}(3, \cdot)\)	n/a	7136	32

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(425))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(425)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 2}\)