Space of modular forms of level 245 and weight 6

• Label: 245.6
• Level: 245
• Weight: 6
• Dimension: 10199
• Nonzero newspaces: 12
• Sturm bound: 28224
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(28224\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(245))\).

	Total	New	Old
Modular forms	12000	10489	1511
Cusp forms	11520	10199	1321
Eisenstein series	480	290	190

Trace form

10199 * q - 28 * q^2 - 70 * q^3 + 174 * q^4 - 176 * q^5 - 710 * q^6 - 268 * q^7 - 858 * q^8 + 3013 * q^9 + 2655 * q^10 + 1094 * q^11 - 9146 * q^12 - 9084 * q^13 - 3516 * q^14 + 2975 * q^15 + 12454 * q^16 + 8000 * q^17 + 14708 * q^18 - 11414 * q^19 - 9067 * q^20 - 2370 * q^21 + 394 * q^22 + 18654 * q^23 + 37494 * q^24 + 12652 * q^25 + 590 * q^26 - 44818 * q^27 - 46420 * q^28 - 67292 * q^29 - 92747 * q^30 - 24030 * q^31 + 96586 * q^32 + 200158 * q^33 + 268770 * q^34 + 69663 * q^35 + 339782 * q^36 + 116036 * q^37 - 143578 * q^38 - 316744 * q^39 - 451999 * q^40 - 334652 * q^41 - 446754 * q^42 - 232230 * q^43 - 187058 * q^44 + 138583 * q^45 + 564626 * q^46 + 504194 * q^47 + 1068496 * q^48 + 403016 * q^49 + 263258 * q^50 + 326770 * q^51 + 252758 * q^52 + 13136 * q^53 - 638330 * q^54 - 72862 * q^55 - 809688 * q^56 - 500530 * q^57 - 1022350 * q^58 - 674602 * q^59 - 1190735 * q^60 - 393742 * q^61 - 165018 * q^62 + 577860 * q^63 + 457414 * q^64 + 311143 * q^65 + 1333034 * q^66 + 507818 * q^67 + 664678 * q^68 + 524622 * q^69 + 713835 * q^70 + 615358 * q^71 + 1456122 * q^72 + 904920 * q^73 + 739618 * q^74 - 120811 * q^75 - 654134 * q^76 - 195930 * q^77 - 1689902 * q^78 - 1065522 * q^79 - 715408 * q^80 - 175487 * q^81 - 894184 * q^82 - 1353582 * q^83 - 3003156 * q^84 - 109119 * q^85 - 1127212 * q^86 - 1146274 * q^87 - 2060820 * q^88 - 712596 * q^89 - 1418212 * q^90 - 237746 * q^91 - 1458960 * q^92 + 393318 * q^93 + 601788 * q^94 + 389605 * q^95 + 5427332 * q^96 + 2631178 * q^97 + 5712912 * q^98 + 2785820 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(245))\)

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
245.6.a	\(\chi_{245}(1, \cdot)\)	245.6.a.a	1	1
		245.6.a.b	1
		245.6.a.c	2
		245.6.a.d	3
		245.6.a.e	4
		245.6.a.f	5
		245.6.a.g	5
		245.6.a.h	6
		245.6.a.i	6
		245.6.a.j	8
		245.6.a.k	8
		245.6.a.l	10
		245.6.a.m	10
245.6.b	\(\chi_{245}(99, \cdot)\)	245.6.b.a	2	1
		245.6.b.b	2
		245.6.b.c	12
		245.6.b.d	14
		245.6.b.e	18
		245.6.b.f	18
		245.6.b.g	32
245.6.e	\(\chi_{245}(116, \cdot)\)	n/a	132	2
245.6.f	\(\chi_{245}(48, \cdot)\)	n/a	192	2
245.6.j	\(\chi_{245}(79, \cdot)\)	n/a	192	2
245.6.k	\(\chi_{245}(36, \cdot)\)	n/a	552	6
245.6.l	\(\chi_{245}(68, \cdot)\)	n/a	384	4
245.6.p	\(\chi_{245}(29, \cdot)\)	n/a	828	6
245.6.q	\(\chi_{245}(11, \cdot)\)	n/a	1128	12
245.6.s	\(\chi_{245}(13, \cdot)\)	n/a	1656	12
245.6.t	\(\chi_{245}(4, \cdot)\)	n/a	1656	12
245.6.x	\(\chi_{245}(3, \cdot)\)	n/a	3312	24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces

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