Space of modular forms of level 725 and weight 6

• Label: 725.6
• Level: 725
• Weight: 6
• Dimension: 95991
• Nonzero newspaces: 24
• Sturm bound: 252000
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 24 \)
Sturm bound:			\(252000\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(725))\).

	Total	New	Old
Modular forms	105784	97097	8687
Cusp forms	104216	95991	8225
Eisenstein series	1568	1106	462

Trace form

95991 * q - 154 * q^2 - 178 * q^3 - 370 * q^4 - 334 * q^5 + 766 * q^6 + 606 * q^7 - 642 * q^8 - 2294 * q^9 - 984 * q^10 + 1166 * q^11 + 286 * q^12 + 982 * q^13 + 4542 * q^14 + 2236 * q^15 + 446 * q^16 - 3054 * q^17 - 18178 * q^18 - 15242 * q^19 - 20724 * q^20 - 7774 * q^21 + 34222 * q^22 + 38176 * q^23 + 118898 * q^24 + 37806 * q^25 + 10006 * q^26 - 15040 * q^27 - 102064 * q^28 - 70032 * q^29 - 108108 * q^30 - 9574 * q^31 - 36898 * q^32 + 19408 * q^33 + 113522 * q^34 + 80536 * q^35 + 246126 * q^36 + 76630 * q^37 + 144546 * q^38 - 94206 * q^39 - 179704 * q^40 - 123234 * q^41 - 408106 * q^42 - 125058 * q^43 - 225884 * q^44 + 35346 * q^45 + 4836 * q^46 + 137314 * q^47 + 865330 * q^48 + 565136 * q^49 + 504676 * q^50 + 247322 * q^51 + 280978 * q^52 + 109289 * q^53 - 216336 * q^54 - 182484 * q^55 - 627484 * q^56 - 774920 * q^57 - 841730 * q^58 - 407696 * q^59 - 195204 * q^60 + 3022 * q^61 - 169388 * q^62 - 750 * q^63 + 94556 * q^64 - 272554 * q^65 + 462158 * q^66 + 321222 * q^67 + 377076 * q^68 + 610730 * q^69 + 235076 * q^70 + 179392 * q^71 + 716932 * q^72 - 177025 * q^73 + 490960 * q^74 + 621356 * q^75 + 1485754 * q^76 + 950604 * q^77 + 1051898 * q^78 + 440226 * q^79 - 4204 * q^80 - 279886 * q^81 + 498430 * q^82 - 444302 * q^83 - 2619852 * q^84 - 1362554 * q^85 - 3023288 * q^86 - 1625792 * q^87 - 4243176 * q^88 - 1536282 * q^89 - 1509044 * q^90 - 311438 * q^91 + 1085574 * q^92 + 927042 * q^93 + 1520478 * q^94 + 847756 * q^95 + 1145212 * q^96 + 1164325 * q^97 + 3540436 * q^98 + 3084044 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(725))\)

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
725.6.a	\(\chi_{725}(1, \cdot)\)	725.6.a.a	4	1
		725.6.a.b	7
		725.6.a.c	11
		725.6.a.d	11
		725.6.a.e	13
		725.6.a.f	13
		725.6.a.g	23
		725.6.a.h	23
		725.6.a.i	23
		725.6.a.j	23
		725.6.a.k	32
		725.6.a.l	38
725.6.b	\(\chi_{725}(349, \cdot)\)	n/a	210	1
725.6.c	\(\chi_{725}(376, \cdot)\)	n/a	234	1
725.6.d	\(\chi_{725}(724, \cdot)\)	n/a	224	1
725.6.e	\(\chi_{725}(157, \cdot)\)	n/a	446	2
725.6.j	\(\chi_{725}(307, \cdot)\)	n/a	446	2
725.6.k	\(\chi_{725}(146, \cdot)\)	n/a	1400	4
725.6.l	\(\chi_{725}(226, \cdot)\)	n/a	1410	6
725.6.m	\(\chi_{725}(144, \cdot)\)	n/a	1488	4
725.6.n	\(\chi_{725}(59, \cdot)\)	n/a	1400	4
725.6.o	\(\chi_{725}(86, \cdot)\)	n/a	1496	4
725.6.p	\(\chi_{725}(149, \cdot)\)	n/a	1344	6
725.6.q	\(\chi_{725}(51, \cdot)\)	n/a	1404	6
725.6.r	\(\chi_{725}(24, \cdot)\)	n/a	1332	6
725.6.s	\(\chi_{725}(17, \cdot)\)	n/a	2984	8
725.6.x	\(\chi_{725}(12, \cdot)\)	n/a	2984	8
725.6.y	\(\chi_{725}(18, \cdot)\)	n/a	2676	12
725.6.bd	\(\chi_{725}(43, \cdot)\)	n/a	2676	12
725.6.be	\(\chi_{725}(16, \cdot)\)	n/a	8928	24
725.6.bf	\(\chi_{725}(6, \cdot)\)	n/a	8976	24
725.6.bg	\(\chi_{725}(54, \cdot)\)	n/a	8976	24
725.6.bh	\(\chi_{725}(4, \cdot)\)	n/a	8928	24
725.6.bi	\(\chi_{725}(3, \cdot)\)	n/a	17904	48
725.6.bn	\(\chi_{725}(2, \cdot)\)	n/a	17904	48

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(725))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(725)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 2}\)