Space of modular forms of level 325 and weight 6

• Label: 325.6
• Level: 325
• Weight: 6
• Dimension: 18899
• Nonzero newspaces: 24
• Sturm bound: 50400
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(50400\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(325))\).

	Total	New	Old
Modular forms	21336	19349	1987
Cusp forms	20664	18899	1765
Eisenstein series	672	450	222

Trace form

18899 * q - 50 * q^2 - 74 * q^3 - 266 * q^4 - 206 * q^5 + 934 * q^6 + 412 * q^7 + 38 * q^8 - 1542 * q^9 - 856 * q^10 + 800 * q^11 - 2496 * q^12 - 1068 * q^13 + 4040 * q^14 + 2364 * q^15 + 5734 * q^16 - 4147 * q^17 - 14636 * q^18 - 10150 * q^19 - 20596 * q^20 - 10800 * q^21 + 18508 * q^22 + 27058 * q^23 + 67690 * q^24 + 37934 * q^25 - 6276 * q^26 - 2912 * q^27 - 80576 * q^28 - 97333 * q^29 - 107756 * q^30 + 26156 * q^31 + 28136 * q^32 + 28872 * q^33 + 89286 * q^34 + 80664 * q^35 + 23274 * q^36 + 25891 * q^37 + 93892 * q^38 - 96012 * q^39 - 179672 * q^40 - 125787 * q^41 - 341888 * q^42 - 40488 * q^43 + 25756 * q^44 + 35474 * q^45 + 114554 * q^46 + 127172 * q^47 + 618138 * q^48 + 332178 * q^49 + 642996 * q^50 + 414540 * q^51 + 30000 * q^52 - 86942 * q^53 - 933184 * q^54 - 454444 * q^55 - 1205384 * q^56 - 1095064 * q^57 - 781626 * q^58 - 279488 * q^59 + 86012 * q^60 + 449009 * q^61 + 491698 * q^62 + 890768 * q^63 + 1003108 * q^64 + 250715 * q^65 + 1138844 * q^66 + 457070 * q^67 + 771600 * q^68 + 589528 * q^69 + 38788 * q^70 + 364842 * q^71 - 1040892 * q^72 - 634254 * q^73 - 1384646 * q^74 - 213596 * q^75 - 1210506 * q^76 - 260652 * q^77 - 588332 * q^78 + 714172 * q^79 + 877588 * q^80 + 1541070 * q^81 + 1505326 * q^82 - 80236 * q^83 - 1088680 * q^84 - 1362426 * q^85 - 1923364 * q^86 - 2235790 * q^87 - 2880128 * q^88 - 759672 * q^89 - 1508916 * q^90 + 381094 * q^91 + 1253120 * q^92 + 1185352 * q^93 + 925722 * q^94 + 847884 * q^95 + 183056 * q^96 + 1639358 * q^97 + 2170818 * q^98 + 1811076 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(325))\)

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
325.6.a	\(\chi_{325}(1, \cdot)\)	325.6.a.a	1	1
		325.6.a.b	2
		325.6.a.c	3
		325.6.a.d	3
		325.6.a.e	4
		325.6.a.f	6
		325.6.a.g	6
		325.6.a.h	9
		325.6.a.i	9
		325.6.a.j	11
		325.6.a.k	11
		325.6.a.l	15
		325.6.a.m	15
325.6.b	\(\chi_{325}(274, \cdot)\)	325.6.b.a	2	1
		325.6.b.b	4
		325.6.b.c	6
		325.6.b.d	6
		325.6.b.e	8
		325.6.b.f	12
		325.6.b.g	12
		325.6.b.h	18
		325.6.b.i	22
325.6.c	\(\chi_{325}(51, \cdot)\)	n/a	108	1
325.6.d	\(\chi_{325}(324, \cdot)\)	n/a	104	1
325.6.e	\(\chi_{325}(126, \cdot)\)	n/a	216	2
325.6.f	\(\chi_{325}(18, \cdot)\)	n/a	206	2
325.6.k	\(\chi_{325}(57, \cdot)\)	n/a	206	2
325.6.l	\(\chi_{325}(66, \cdot)\)	n/a	600	4
325.6.m	\(\chi_{325}(49, \cdot)\)	n/a	208	2
325.6.n	\(\chi_{325}(101, \cdot)\)	n/a	214	2
325.6.o	\(\chi_{325}(74, \cdot)\)	n/a	204	2
325.6.p	\(\chi_{325}(64, \cdot)\)	n/a	688	4
325.6.q	\(\chi_{325}(116, \cdot)\)	n/a	696	4
325.6.r	\(\chi_{325}(14, \cdot)\)	n/a	600	4
325.6.s	\(\chi_{325}(32, \cdot)\)	n/a	412	4
325.6.x	\(\chi_{325}(7, \cdot)\)	n/a	412	4
325.6.y	\(\chi_{325}(16, \cdot)\)	n/a	1376	8
325.6.z	\(\chi_{325}(8, \cdot)\)	n/a	1384	8
325.6.be	\(\chi_{325}(47, \cdot)\)	n/a	1384	8
325.6.bf	\(\chi_{325}(9, \cdot)\)	n/a	1392	8
325.6.bg	\(\chi_{325}(36, \cdot)\)	n/a	1392	8
325.6.bh	\(\chi_{325}(4, \cdot)\)	n/a	1376	8
325.6.bi	\(\chi_{325}(28, \cdot)\)	n/a	2768	16
325.6.bn	\(\chi_{325}(2, \cdot)\)	n/a	2768	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(325))\) into lower level spaces

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