Space of modular forms of level 325 and weight 4

• Label: 325.4
• Level: 325
• Weight: 4
• Dimension: 11249
• Nonzero newspaces: 24
• Sturm bound: 33600
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(33600\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(325))\).

	Total	New	Old
Modular forms	12936	11699	1237
Cusp forms	12264	11249	1015
Eisenstein series	672	450	222

Trace form

11249 * q - 74 * q^2 - 50 * q^3 - 26 * q^4 - 86 * q^5 - 122 * q^6 - 70 * q^7 - 130 * q^8 - 150 * q^9 - 36 * q^10 + 98 * q^11 + 240 * q^12 - 112 * q^14 - 96 * q^15 + 166 * q^16 + 497 * q^17 + 382 * q^18 + 138 * q^19 - 436 * q^20 - 522 * q^21 - 1620 * q^22 - 1022 * q^23 - 1862 * q^24 - 1466 * q^25 + 396 * q^26 - 788 * q^27 - 1360 * q^28 - 847 * q^29 + 484 * q^30 - 114 * q^31 + 2552 * q^32 + 1518 * q^33 + 2130 * q^34 + 1584 * q^35 + 1770 * q^36 + 2259 * q^37 + 4684 * q^38 + 2292 * q^39 + 3928 * q^40 + 447 * q^41 + 520 * q^42 + 730 * q^43 - 1460 * q^44 - 4486 * q^45 - 2454 * q^46 - 5422 * q^47 - 9942 * q^48 - 4704 * q^49 - 7344 * q^50 + 5316 * q^51 + 10660 * q^52 + 4018 * q^53 + 7976 * q^54 - 44 * q^55 + 3400 * q^56 + 1106 * q^57 + 236 * q^58 + 4138 * q^59 + 10172 * q^60 - 645 * q^61 + 2890 * q^62 - 8182 * q^63 - 14364 * q^64 - 4285 * q^65 - 25972 * q^66 - 13042 * q^67 - 24300 * q^68 - 19598 * q^69 - 13372 * q^70 - 3570 * q^71 - 20220 * q^72 - 6018 * q^73 - 10904 * q^74 - 6296 * q^75 + 10262 * q^76 + 3456 * q^77 + 31540 * q^78 + 11000 * q^79 + 3028 * q^80 + 25296 * q^81 + 22636 * q^82 + 18062 * q^83 + 39368 * q^84 + 19194 * q^85 + 6956 * q^86 + 12962 * q^87 + 24704 * q^88 + 10872 * q^89 + 16224 * q^90 - 1488 * q^91 + 2528 * q^92 - 13430 * q^93 - 15630 * q^94 - 13716 * q^95 - 8128 * q^96 - 22742 * q^97 - 24870 * q^98 - 21546 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(325))\)

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
325.4.a	\(\chi_{325}(1, \cdot)\)	325.4.a.a	1	1
		325.4.a.b	1
		325.4.a.c	1
		325.4.a.d	1
		325.4.a.e	2
		325.4.a.f	2
		325.4.a.g	2
		325.4.a.h	2
		325.4.a.i	5
		325.4.a.j	5
		325.4.a.k	5
		325.4.a.l	7
		325.4.a.m	7
		325.4.a.n	8
		325.4.a.o	8
325.4.b	\(\chi_{325}(274, \cdot)\)	325.4.b.a	2	1
		325.4.b.b	2
		325.4.b.c	4
		325.4.b.d	4
		325.4.b.e	4
		325.4.b.f	4
		325.4.b.g	10
		325.4.b.h	10
		325.4.b.i	14
325.4.c	\(\chi_{325}(51, \cdot)\)	325.4.c.a	2	1
		325.4.c.b	2
		325.4.c.c	2
		325.4.c.d	14
		325.4.c.e	14
		325.4.c.f	14
		325.4.c.g	16
325.4.d	\(\chi_{325}(324, \cdot)\)	325.4.d.a	2	1
		325.4.d.b	2
		325.4.d.c	14
		325.4.d.d	14
		325.4.d.e	28
325.4.e	\(\chi_{325}(126, \cdot)\)	n/a	126	2
325.4.f	\(\chi_{325}(18, \cdot)\)	n/a	122	2
325.4.k	\(\chi_{325}(57, \cdot)\)	n/a	122	2
325.4.l	\(\chi_{325}(66, \cdot)\)	n/a	360	4
325.4.m	\(\chi_{325}(49, \cdot)\)	n/a	120	2
325.4.n	\(\chi_{325}(101, \cdot)\)	n/a	128	2
325.4.o	\(\chi_{325}(74, \cdot)\)	n/a	124	2
325.4.p	\(\chi_{325}(64, \cdot)\)	n/a	416	4
325.4.q	\(\chi_{325}(116, \cdot)\)	n/a	408	4
325.4.r	\(\chi_{325}(14, \cdot)\)	n/a	360	4
325.4.s	\(\chi_{325}(32, \cdot)\)	n/a	244	4
325.4.x	\(\chi_{325}(7, \cdot)\)	n/a	244	4
325.4.y	\(\chi_{325}(16, \cdot)\)	n/a	832	8
325.4.z	\(\chi_{325}(8, \cdot)\)	n/a	824	8
325.4.be	\(\chi_{325}(47, \cdot)\)	n/a	824	8
325.4.bf	\(\chi_{325}(9, \cdot)\)	n/a	816	8
325.4.bg	\(\chi_{325}(36, \cdot)\)	n/a	816	8
325.4.bh	\(\chi_{325}(4, \cdot)\)	n/a	832	8
325.4.bi	\(\chi_{325}(28, \cdot)\)	n/a	1648	16
325.4.bn	\(\chi_{325}(2, \cdot)\)	n/a	1648	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(325))\) into lower level spaces

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