Space of modular forms of level 245 and weight 4

• Label: 245.4
• Level: 245
• Weight: 4
• Dimension: 6061
• Nonzero newspaces: 12
• Newform subspaces: 61
• Sturm bound: 18816
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 61 \)
Sturm bound:			\(18816\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(245))\).

	Total	New	Old
Modular forms	7296	6351	945
Cusp forms	6816	6061	755
Eisenstein series	480	290	190

Trace form

6061 * q - 34 * q^2 - 52 * q^3 - 22 * q^4 - 26 * q^5 + 34 * q^6 + 12 * q^7 - 162 * q^8 - 221 * q^9 - 79 * q^10 - 58 * q^11 + 166 * q^12 - 56 * q^13 + 12 * q^14 + 53 * q^15 + 86 * q^16 + 308 * q^17 - 10 * q^18 - 554 * q^19 - 415 * q^20 - 564 * q^21 - 206 * q^22 + 732 * q^23 + 2070 * q^24 + 1744 * q^25 + 1898 * q^26 + 1586 * q^27 + 732 * q^28 - 248 * q^29 - 2147 * q^30 - 1782 * q^31 - 5078 * q^32 - 3590 * q^33 - 3914 * q^34 - 1338 * q^35 - 2638 * q^36 + 1076 * q^37 + 2726 * q^38 + 2510 * q^39 + 3225 * q^40 + 4528 * q^41 + 1302 * q^42 + 244 * q^43 - 1298 * q^44 + 724 * q^45 - 4566 * q^46 - 2272 * q^47 - 10928 * q^48 - 7800 * q^49 - 5716 * q^50 - 6926 * q^51 - 10882 * q^52 - 4228 * q^53 + 910 * q^54 + 5543 * q^55 + 5784 * q^56 + 14162 * q^57 + 19310 * q^58 + 13286 * q^59 + 16345 * q^60 + 10120 * q^61 + 11166 * q^62 + 7080 * q^63 + 358 * q^64 - 5813 * q^65 - 16534 * q^66 - 12672 * q^67 - 19154 * q^68 - 22686 * q^69 - 12849 * q^70 - 12686 * q^71 - 21774 * q^72 - 10196 * q^73 - 14786 * q^74 - 4687 * q^75 - 5542 * q^76 - 504 * q^77 + 7570 * q^78 + 6786 * q^79 + 25376 * q^80 + 43855 * q^81 + 47276 * q^82 + 33624 * q^83 + 54780 * q^84 + 22313 * q^85 + 39836 * q^86 + 29426 * q^87 + 32268 * q^88 + 16188 * q^89 + 10646 * q^90 - 6774 * q^91 - 1632 * q^92 - 38550 * q^93 - 34436 * q^94 - 22721 * q^95 - 81004 * q^96 - 28678 * q^97 - 63936 * q^98 - 47080 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)

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
245.4.a	\(\chi_{245}(1, \cdot)\)	245.4.a.a	1	1
		245.4.a.b	1
		245.4.a.c	1
		245.4.a.d	1
		245.4.a.e	1
		245.4.a.f	1
		245.4.a.g	2
		245.4.a.h	2
		245.4.a.i	2
		245.4.a.j	2
		245.4.a.k	2
		245.4.a.l	3
		245.4.a.m	5
		245.4.a.n	5
		245.4.a.o	6
		245.4.a.p	6
245.4.b	\(\chi_{245}(99, \cdot)\)	245.4.b.a	2	1
		245.4.b.b	4
		245.4.b.c	8
		245.4.b.d	10
		245.4.b.e	10
		245.4.b.f	10
		245.4.b.g	12
245.4.e	\(\chi_{245}(116, \cdot)\)	245.4.e.a	2	2
		245.4.e.b	2
		245.4.e.c	2
		245.4.e.d	2
		245.4.e.e	2
		245.4.e.f	2
		245.4.e.g	2
		245.4.e.h	4
		245.4.e.i	4
		245.4.e.j	4
		245.4.e.k	4
		245.4.e.l	4
		245.4.e.m	6
		245.4.e.n	6
		245.4.e.o	10
		245.4.e.p	12
		245.4.e.q	12
245.4.f	\(\chi_{245}(48, \cdot)\)	245.4.f.a	40	2
		245.4.f.b	72
245.4.j	\(\chi_{245}(79, \cdot)\)	245.4.j.a	4	2
		245.4.j.b	8
		245.4.j.c	16
		245.4.j.d	20
		245.4.j.e	20
		245.4.j.f	20
		245.4.j.g	24
245.4.k	\(\chi_{245}(36, \cdot)\)	245.4.k.a	162	6
		245.4.k.b	174
245.4.l	\(\chi_{245}(68, \cdot)\)	245.4.l.a	8	4
		245.4.l.b	32
		245.4.l.c	40
		245.4.l.d	144
245.4.p	\(\chi_{245}(29, \cdot)\)	245.4.p.a	492	6
245.4.q	\(\chi_{245}(11, \cdot)\)	245.4.q.a	324	12
		245.4.q.b	348
245.4.s	\(\chi_{245}(13, \cdot)\)	245.4.s.a	984	12
245.4.t	\(\chi_{245}(4, \cdot)\)	245.4.t.a	984	12
245.4.x	\(\chi_{245}(3, \cdot)\)	245.4.x.a	1968	24

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(245)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)