Space of modular forms of level 245 and weight 3

• Label: 245.3
• Level: 245
• Weight: 3
• Dimension: 3992
• Nonzero newspaces: 12
• Newform subspaces: 29
• Sturm bound: 14112
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 29 \)
Sturm bound:			\(14112\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(245))\).

	Total	New	Old
Modular forms	4944	4284	660
Cusp forms	4464	3992	472
Eisenstein series	480	292	188

Trace form

3992 * q - 30 * q^2 - 18 * q^3 + 2 * q^4 - 39 * q^5 - 78 * q^6 - 44 * q^7 - 42 * q^8 + 18 * q^9 - 39 * q^10 - 102 * q^11 - 18 * q^12 - 18 * q^13 + 12 * q^14 - 69 * q^15 - 122 * q^16 - 18 * q^17 - 126 * q^18 - 18 * q^19 - 39 * q^20 - 102 * q^21 + 42 * q^22 + 54 * q^23 - 402 * q^24 - 155 * q^25 - 462 * q^26 - 522 * q^27 - 388 * q^28 - 486 * q^29 - 615 * q^30 - 222 * q^31 - 126 * q^32 - 138 * q^33 - 42 * q^34 - 15 * q^35 - 222 * q^36 - 570 * q^37 - 474 * q^38 - 300 * q^39 - 183 * q^40 - 330 * q^41 - 462 * q^42 + 214 * q^43 - 186 * q^44 + 438 * q^45 - 222 * q^46 + 210 * q^47 + 804 * q^48 + 236 * q^49 - 264 * q^50 + 426 * q^51 + 830 * q^52 + 378 * q^53 + 630 * q^54 + 24 * q^55 + 1332 * q^56 - 426 * q^57 + 198 * q^58 - 54 * q^59 - 687 * q^60 + 44 * q^61 - 354 * q^62 + 108 * q^63 - 682 * q^64 - 615 * q^65 - 942 * q^66 - 874 * q^67 - 378 * q^68 - 42 * q^69 + 129 * q^70 + 510 * q^71 + 1050 * q^72 + 750 * q^73 + 1758 * q^74 + 1113 * q^75 + 1938 * q^76 + 630 * q^77 + 1266 * q^78 + 1526 * q^79 + 882 * q^80 - 714 * q^81 - 48 * q^82 - 1026 * q^83 - 5028 * q^84 + 459 * q^85 - 3240 * q^86 - 3738 * q^87 - 4872 * q^88 - 3162 * q^89 - 4656 * q^90 - 1734 * q^91 - 4596 * q^92 - 3882 * q^93 - 3072 * q^94 - 2103 * q^95 - 3648 * q^96 - 1068 * q^97 - 600 * q^98 - 576 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(245))\)

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
245.3.c	\(\chi_{245}(244, \cdot)\)	245.3.c.a	12	1
		245.3.c.b	24
245.3.d	\(\chi_{245}(146, \cdot)\)	245.3.d.a	12	1
		245.3.d.b	16
245.3.g	\(\chi_{245}(148, \cdot)\)	245.3.g.a	12	2
		245.3.g.b	12
		245.3.g.c	12
		245.3.g.d	12
		245.3.g.e	24
245.3.h	\(\chi_{245}(31, \cdot)\)	245.3.h.a	4	2
		245.3.h.b	4
		245.3.h.c	12
		245.3.h.d	32
245.3.i	\(\chi_{245}(19, \cdot)\)	245.3.i.a	2	2
		245.3.i.b	2
		245.3.i.c	8
		245.3.i.d	12
		245.3.i.e	48
245.3.m	\(\chi_{245}(18, \cdot)\)	245.3.m.a	24	4
		245.3.m.b	24
		245.3.m.c	24
		245.3.m.d	24
		245.3.m.e	48
245.3.n	\(\chi_{245}(6, \cdot)\)	245.3.n.a	216	6
245.3.o	\(\chi_{245}(34, \cdot)\)	245.3.o.a	324	6
245.3.r	\(\chi_{245}(8, \cdot)\)	245.3.r.a	648	12
245.3.u	\(\chi_{245}(24, \cdot)\)	245.3.u.a	648	12
245.3.v	\(\chi_{245}(26, \cdot)\)	245.3.v.a	456	12
245.3.w	\(\chi_{245}(2, \cdot)\)	245.3.w.a	1296	24

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces

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