Space of modular forms of level 245 and weight 10

• Label: 245.10
• Level: 245
• Weight: 10
• Dimension: 18475
• Nonzero newspaces: 12
• Sturm bound: 47040
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(47040\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(245))\).

	Total	New	Old
Modular forms	21408	18765	2643
Cusp forms	20928	18475	2453
Eisenstein series	480	290	190

Trace form

18475 * q - 48 * q^2 + 764 * q^3 - 802 * q^4 + 3424 * q^5 - 32822 * q^6 + 2700 * q^7 + 191142 * q^8 - 195359 * q^9 - 170805 * q^10 + 384006 * q^11 + 552550 * q^12 - 1464884 * q^13 + 50580 * q^14 - 73915 * q^15 + 4704166 * q^16 + 4417464 * q^17 - 4824784 * q^18 - 4816938 * q^19 - 5967707 * q^20 - 2299476 * q^21 - 2843494 * q^22 + 19628700 * q^23 + 41307894 * q^24 - 9545258 * q^25 - 39868554 * q^26 - 33699166 * q^27 - 10437780 * q^28 + 20712084 * q^29 - 56980187 * q^30 + 50123146 * q^31 + 72517386 * q^32 - 35008934 * q^33 - 101908614 * q^34 + 4597998 * q^35 + 282506102 * q^36 - 17267736 * q^37 + 68875302 * q^38 - 56084242 * q^39 + 110952001 * q^40 - 169963908 * q^41 - 270430482 * q^42 + 130323748 * q^43 - 97735602 * q^44 - 228605882 * q^45 + 174441730 * q^46 + 192027936 * q^47 + 1050020176 * q^48 + 736428096 * q^49 - 226120842 * q^50 - 39476558 * q^51 - 1546775178 * q^52 - 758558304 * q^53 - 1648502954 * q^54 - 480985097 * q^55 + 375492840 * q^56 + 41454626 * q^57 + 3450291034 * q^58 + 1819334214 * q^59 + 2430740305 * q^60 - 1134702780 * q^61 - 2142633066 * q^62 - 700968216 * q^63 - 2696093498 * q^64 - 2038924057 * q^65 - 3820418710 * q^66 - 780530176 * q^67 + 8332726470 * q^68 + 9456940146 * q^69 + 4076127555 * q^70 - 1809362478 * q^71 - 7776868422 * q^72 - 6482219696 * q^73 - 5874112950 * q^74 - 4528667071 * q^75 - 1157649462 * q^76 + 2394310464 * q^77 + 4374611986 * q^78 + 877830466 * q^79 + 9025828912 * q^80 - 7479397739 * q^81 - 5994472112 * q^82 - 2174495208 * q^83 + 16974273132 * q^84 - 4275078339 * q^85 + 8254928772 * q^86 + 5040631010 * q^87 - 15310045332 * q^88 - 2697791544 * q^89 - 13874086072 * q^90 - 6213070806 * q^91 + 5766588816 * q^92 + 575592618 * q^93 + 14110394076 * q^94 - 1418382625 * q^95 + 19919799236 * q^96 - 3676494306 * q^97 + 31157379696 * q^98 - 4435245064 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(245))\)

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
245.10.a	\(\chi_{245}(1, \cdot)\)	245.10.a.a	1	1
		245.10.a.b	1
		245.10.a.c	2
		245.10.a.d	2
		245.10.a.e	4
		245.10.a.f	5
		245.10.a.g	6
		245.10.a.h	9
		245.10.a.i	9
		245.10.a.j	11
		245.10.a.k	11
		245.10.a.l	13
		245.10.a.m	13
		245.10.a.n	18
		245.10.a.o	18
245.10.b	\(\chi_{245}(99, \cdot)\)	n/a	180	1
245.10.e	\(\chi_{245}(116, \cdot)\)	n/a	240	2
245.10.f	\(\chi_{245}(48, \cdot)\)	n/a	352	2
245.10.j	\(\chi_{245}(79, \cdot)\)	n/a	352	2
245.10.k	\(\chi_{245}(36, \cdot)\)	n/a	1008	6
245.10.l	\(\chi_{245}(68, \cdot)\)	n/a	704	4
245.10.p	\(\chi_{245}(29, \cdot)\)	n/a	1500	6
245.10.q	\(\chi_{245}(11, \cdot)\)	n/a	2016	12
245.10.s	\(\chi_{245}(13, \cdot)\)	n/a	3000	12
245.10.t	\(\chi_{245}(4, \cdot)\)	n/a	3000	12
245.10.x	\(\chi_{245}(3, \cdot)\)	n/a	6000	24

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(245)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 1}\)