Space of modular forms of level 575 and weight 4

• Label: 575.4
• Level: 575
• Weight: 4
• Dimension: 35929
• Nonzero newspaces: 12
• Sturm bound: 105600
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(105600\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(575))\).

	Total	New	Old
Modular forms	40216	36789	3427
Cusp forms	38984	35929	3055
Eisenstein series	1232	860	372

Trace form

35929 * q - 139 * q^2 - 115 * q^3 - 91 * q^4 - 166 * q^5 - 227 * q^6 - 99 * q^7 - 123 * q^8 - 215 * q^9 - 116 * q^10 - 67 * q^11 - 59 * q^12 - 275 * q^13 - 219 * q^14 - 176 * q^15 - 379 * q^16 + 533 * q^17 + 1233 * q^18 + 627 * q^19 - 516 * q^20 + 33 * q^21 - 1602 * q^22 - 245 * q^23 - 1806 * q^24 - 1546 * q^25 - 447 * q^26 - 1537 * q^27 - 1723 * q^28 - 703 * q^29 + 404 * q^30 - 457 * q^31 + 1645 * q^32 + 1085 * q^33 + 847 * q^34 + 1504 * q^35 - 654 * q^36 + 823 * q^37 + 2652 * q^38 + 4585 * q^39 + 3944 * q^40 + 1363 * q^41 + 4715 * q^42 + 2801 * q^43 + 1464 * q^44 - 4566 * q^45 + 2151 * q^46 - 3870 * q^47 - 9351 * q^48 - 3563 * q^49 - 9176 * q^50 - 5167 * q^51 - 8589 * q^52 - 3687 * q^53 - 11563 * q^54 - 1996 * q^55 - 9394 * q^56 - 4143 * q^57 - 4056 * q^58 + 4495 * q^59 + 22764 * q^60 + 5901 * q^61 + 23861 * q^62 + 17855 * q^63 + 17473 * q^64 + 3734 * q^65 + 7156 * q^66 + 393 * q^67 + 1994 * q^68 + 215 * q^69 - 8732 * q^70 - 97 * q^71 - 11528 * q^72 - 8339 * q^73 - 18180 * q^74 - 11896 * q^75 - 14830 * q^76 - 15691 * q^77 - 22229 * q^78 - 6751 * q^79 - 11836 * q^80 - 1619 * q^81 + 8255 * q^82 + 10715 * q^83 + 20699 * q^84 + 19114 * q^85 + 11127 * q^86 + 26169 * q^87 + 36957 * q^88 + 20137 * q^89 + 16144 * q^90 + 10490 * q^91 + 12608 * q^92 + 2298 * q^93 - 5652 * q^94 - 2092 * q^95 + 74572 * q^96 + 23759 * q^97 + 30765 * q^98 + 26323 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(575))\)

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
575.4.a	\(\chi_{575}(1, \cdot)\)	575.4.a.a	1	1
		575.4.a.b	1
		575.4.a.c	1
		575.4.a.d	1
		575.4.a.e	1
		575.4.a.f	1
		575.4.a.g	1
		575.4.a.h	2
		575.4.a.i	4
		575.4.a.j	5
		575.4.a.k	5
		575.4.a.l	7
		575.4.a.m	7
		575.4.a.n	8
		575.4.a.o	13
		575.4.a.p	13
		575.4.a.q	17
		575.4.a.r	17
575.4.b	\(\chi_{575}(24, \cdot)\)	575.4.b.a	2	1
		575.4.b.b	2
		575.4.b.c	2
		575.4.b.d	2
		575.4.b.e	2
		575.4.b.f	4
		575.4.b.g	8
		575.4.b.h	10
		575.4.b.i	10
		575.4.b.j	14
		575.4.b.k	16
		575.4.b.l	26
575.4.e	\(\chi_{575}(68, \cdot)\)	n/a	212	2
575.4.g	\(\chi_{575}(116, \cdot)\)	n/a	656	4
575.4.i	\(\chi_{575}(139, \cdot)\)	n/a	664	4
575.4.k	\(\chi_{575}(26, \cdot)\)	n/a	1110	10
575.4.m	\(\chi_{575}(22, \cdot)\)	n/a	1424	8
575.4.p	\(\chi_{575}(49, \cdot)\)	n/a	1060	10
575.4.r	\(\chi_{575}(7, \cdot)\)	n/a	2120	20
575.4.s	\(\chi_{575}(6, \cdot)\)	n/a	7120	40
575.4.u	\(\chi_{575}(4, \cdot)\)	n/a	7120	40
575.4.w	\(\chi_{575}(17, \cdot)\)	n/a	14240	80

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(575))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(575)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 2}\)