Space of modular forms of level 325 and weight 8

• Label: 325.8
• Level: 325
• Weight: 8
• Dimension: 26549
• Nonzero newspaces: 24
• Sturm bound: 67200
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(67200\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(325))\).

	Total	New	Old
Modular forms	29736	26999	2737
Cusp forms	29064	26549	2515
Eisenstein series	672	450	222

Trace form

26549 * q - 34 * q^2 - 170 * q^3 + 694 * q^4 - 26 * q^5 - 4250 * q^6 - 8548 * q^7 + 13670 * q^8 + 25938 * q^9 + 3024 * q^10 - 31896 * q^11 - 72000 * q^12 + 29700 * q^13 + 147320 * q^14 + 17724 * q^15 - 69018 * q^16 - 351857 * q^17 + 76456 * q^18 + 401274 * q^19 + 619244 * q^20 + 76644 * q^21 + 137820 * q^22 - 794046 * q^23 - 2233430 * q^24 - 893766 * q^25 + 556812 * q^26 + 1945552 * q^27 + 2121152 * q^28 + 736581 * q^29 + 1890004 * q^30 + 927980 * q^31 - 2941176 * q^32 - 4072668 * q^33 - 4063618 * q^34 + 278744 * q^35 + 2084826 * q^36 + 2518997 * q^37 + 3778388 * q^38 - 1747884 * q^39 - 5242072 * q^40 + 799123 * q^41 + 5613184 * q^42 + 5236032 * q^43 + 10055212 * q^44 + 6946934 * q^45 - 14937478 * q^46 - 6890348 * q^47 - 11825574 * q^48 + 2914386 * q^49 - 9030964 * q^50 + 3915756 * q^51 - 32918096 * q^52 - 24770794 * q^53 - 3493120 * q^54 + 13268756 * q^55 + 55456648 * q^56 + 67418564 * q^57 + 51051250 * q^58 + 29550792 * q^59 - 21013348 * q^60 - 13373077 * q^61 - 103784622 * q^62 - 91713856 * q^63 - 63641692 * q^64 - 12027935 * q^65 - 25609924 * q^66 + 14862478 * q^67 + 43149200 * q^68 + 54988828 * q^69 + 56354148 * q^70 + 27421610 * q^71 + 120719028 * q^72 + 8542938 * q^73 - 18017802 * q^74 - 64647596 * q^75 - 90680362 * q^76 - 59478756 * q^77 - 121093628 * q^78 - 23054660 * q^79 + 87030548 * q^80 + 127581114 * q^81 + 159042426 * q^82 - 1414164 * q^83 - 90363304 * q^84 - 102128446 * q^85 - 143290980 * q^86 - 152593198 * q^87 + 6085920 * q^88 + 105915948 * q^89 + 120855444 * q^90 + 64116526 * q^91 + 319625760 * q^92 + 266018716 * q^93 + 99215018 * q^94 - 31473716 * q^95 - 270403648 * q^96 - 270425954 * q^97 - 450320750 * q^98 - 286579140 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(325))\)

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
325.8.a	\(\chi_{325}(1, \cdot)\)	325.8.a.a	1	1
		325.8.a.b	2
		325.8.a.c	4
		325.8.a.d	6
		325.8.a.e	6
		325.8.a.f	7
		325.8.a.g	9
		325.8.a.h	13
		325.8.a.i	13
		325.8.a.j	15
		325.8.a.k	15
		325.8.a.l	21
		325.8.a.m	21
325.8.b	\(\chi_{325}(274, \cdot)\)	n/a	126	1
325.8.c	\(\chi_{325}(51, \cdot)\)	n/a	152	1
325.8.d	\(\chi_{325}(324, \cdot)\)	n/a	144	1
325.8.e	\(\chi_{325}(126, \cdot)\)	n/a	304	2
325.8.f	\(\chi_{325}(18, \cdot)\)	n/a	290	2
325.8.k	\(\chi_{325}(57, \cdot)\)	n/a	290	2
325.8.l	\(\chi_{325}(66, \cdot)\)	n/a	840	4
325.8.m	\(\chi_{325}(49, \cdot)\)	n/a	288	2
325.8.n	\(\chi_{325}(101, \cdot)\)	n/a	306	2
325.8.o	\(\chi_{325}(74, \cdot)\)	n/a	292	2
325.8.p	\(\chi_{325}(64, \cdot)\)	n/a	976	4
325.8.q	\(\chi_{325}(116, \cdot)\)	n/a	968	4
325.8.r	\(\chi_{325}(14, \cdot)\)	n/a	840	4
325.8.s	\(\chi_{325}(32, \cdot)\)	n/a	580	4
325.8.x	\(\chi_{325}(7, \cdot)\)	n/a	580	4
325.8.y	\(\chi_{325}(16, \cdot)\)	n/a	1952	8
325.8.z	\(\chi_{325}(8, \cdot)\)	n/a	1944	8
325.8.be	\(\chi_{325}(47, \cdot)\)	n/a	1944	8
325.8.bf	\(\chi_{325}(9, \cdot)\)	n/a	1936	8
325.8.bg	\(\chi_{325}(36, \cdot)\)	n/a	1936	8
325.8.bh	\(\chi_{325}(4, \cdot)\)	n/a	1952	8
325.8.bi	\(\chi_{325}(28, \cdot)\)	n/a	3888	16
325.8.bn	\(\chi_{325}(2, \cdot)\)	n/a	3888	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(325))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(325)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)