Space of modular forms of level 325 and weight 3

• Label: 325.3
• Level: 325
• Weight: 3
• Dimension: 7424
• Nonzero newspaces: 16
• Newform subspaces: 42
• Sturm bound: 25200
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 16 \)
Newform subspaces:			\( 42 \)
Sturm bound:			\(25200\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(325))\).

	Total	New	Old
Modular forms	8736	7876	860
Cusp forms	8064	7424	640
Eisenstein series	672	452	220

Trace form

7424 * q - 58 * q^2 - 58 * q^3 - 58 * q^4 - 76 * q^5 - 90 * q^6 - 48 * q^7 - 22 * q^8 - 34 * q^9 - 76 * q^10 - 84 * q^11 - 52 * q^12 - 80 * q^13 - 160 * q^14 - 76 * q^15 - 298 * q^16 - 204 * q^17 - 322 * q^18 - 242 * q^19 - 356 * q^20 - 132 * q^21 - 128 * q^22 - 74 * q^23 - 6 * q^24 - 16 * q^25 - 208 * q^26 - 28 * q^27 + 388 * q^28 + 190 * q^29 + 404 * q^30 + 216 * q^31 + 508 * q^32 + 200 * q^33 + 322 * q^34 + 144 * q^35 - 106 * q^36 - 200 * q^37 - 712 * q^38 - 396 * q^39 - 1072 * q^40 - 272 * q^41 - 1332 * q^42 - 352 * q^43 - 836 * q^44 - 716 * q^45 - 342 * q^46 - 284 * q^47 - 1286 * q^48 - 144 * q^49 - 64 * q^50 - 1192 * q^51 - 1688 * q^52 - 772 * q^53 - 1464 * q^54 - 244 * q^55 - 1888 * q^56 - 512 * q^57 - 268 * q^58 - 380 * q^59 - 148 * q^60 - 832 * q^61 - 762 * q^62 - 380 * q^63 - 800 * q^64 - 360 * q^65 + 372 * q^66 - 2 * q^67 + 464 * q^68 + 1000 * q^69 + 148 * q^70 + 546 * q^71 + 3840 * q^72 + 1222 * q^73 + 2256 * q^74 + 1404 * q^75 + 3430 * q^76 + 2300 * q^77 + 4124 * q^78 + 1740 * q^79 + 2948 * q^80 + 1238 * q^81 + 324 * q^82 - 312 * q^83 + 1496 * q^84 - 1296 * q^85 - 408 * q^86 - 474 * q^87 - 656 * q^88 + 38 * q^89 - 856 * q^90 - 194 * q^91 - 696 * q^92 - 1052 * q^93 - 2078 * q^94 - 716 * q^95 - 324 * q^96 - 502 * q^97 - 202 * q^98 + 288 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(325))\)

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
325.3.g	\(\chi_{325}(99, \cdot)\)	325.3.g.a	4	2
		325.3.g.b	4
		325.3.g.c	16
		325.3.g.d	16
		325.3.g.e	20
		325.3.g.f	20
325.3.h	\(\chi_{325}(168, \cdot)\)	325.3.h.a	16	2
		325.3.h.b	24
		325.3.h.c	40
325.3.i	\(\chi_{325}(118, \cdot)\)	325.3.i.a	16	2
		325.3.i.b	24
		325.3.i.c	32
325.3.j	\(\chi_{325}(151, \cdot)\)	325.3.j.a	4	2
		325.3.j.b	16
		325.3.j.c	20
		325.3.j.d	20
		325.3.j.e	24
325.3.t	\(\chi_{325}(76, \cdot)\)	325.3.t.a	4	4
		325.3.t.b	36
		325.3.t.c	36
		325.3.t.d	40
		325.3.t.e	48
325.3.u	\(\chi_{325}(68, \cdot)\)	325.3.u.a	40	4
		325.3.u.b	48
		325.3.u.c	72
325.3.v	\(\chi_{325}(43, \cdot)\)	325.3.v.a	40	4
		325.3.v.b	48
		325.3.v.c	72
325.3.w	\(\chi_{325}(24, \cdot)\)	325.3.w.a	4	4
		325.3.w.b	4
		325.3.w.c	36
		325.3.w.d	36
		325.3.w.e	40
		325.3.w.f	40
325.3.ba	\(\chi_{325}(21, \cdot)\)	325.3.ba.a	544	8
325.3.bb	\(\chi_{325}(27, \cdot)\)	325.3.bb.a	480	8
325.3.bc	\(\chi_{325}(12, \cdot)\)	325.3.bc.a	544	8
325.3.bd	\(\chi_{325}(34, \cdot)\)	325.3.bd.a	544	8
325.3.bj	\(\chi_{325}(19, \cdot)\)	325.3.bj.a	1088	16
325.3.bk	\(\chi_{325}(17, \cdot)\)	325.3.bk.a	1088	16
325.3.bl	\(\chi_{325}(3, \cdot)\)	325.3.bl.a	1088	16
325.3.bm	\(\chi_{325}(6, \cdot)\)	325.3.bm.a	1088	16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(325))\) into lower level spaces

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