Space of modular forms of level 49 and weight 10

• Label: 49.10
• Level: 49
• Weight: 10
• Dimension: 822
• Nonzero newspaces: 4
• Newform subspaces: 17
• Sturm bound: 1960
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 49 = 7^{2} \)
Weight:	\( k \)	=	\( 10 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1960\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(49))\).

	Total	New	Old
Modular forms	912	871	41
Cusp forms	852	822	30
Eisenstein series	60	49	11

Trace form

822 * q - 15 * q^2 - 339 * q^3 - 15 * q^4 - 1719 * q^5 + 15543 * q^6 - 1386 * q^7 - 101925 * q^8 + 101373 * q^9 + 100335 * q^10 - 148191 * q^11 - 162729 * q^12 + 731955 * q^13 - 25326 * q^14 - 89163 * q^15 - 1608567 * q^16 - 1754931 * q^17 + 1908165 * q^18 + 1437369 * q^19 + 3597867 * q^20 + 1149666 * q^21 + 3463665 * q^22 - 10605267 * q^23 - 20602809 * q^24 - 7701723 * q^25 + 17466435 * q^26 + 41156559 * q^27 + 16929318 * q^28 - 18741507 * q^29 - 65414049 * q^30 - 49031895 * q^31 - 40486035 * q^32 + 68422413 * q^33 + 138276015 * q^34 + 34642146 * q^35 - 151634169 * q^36 - 52719675 * q^37 - 136851333 * q^38 - 82217667 * q^39 - 194297877 * q^40 + 106922487 * q^41 + 271382181 * q^42 + 55775229 * q^43 + 102903267 * q^44 - 78773421 * q^45 - 310261617 * q^46 - 42610215 * q^47 - 423197478 * q^48 - 368214084 * q^49 - 130221750 * q^50 + 34430661 * q^51 + 846164403 * q^52 + 379630845 * q^53 + 966803079 * q^54 + 646715325 * q^55 - 663558756 * q^56 - 311758059 * q^57 - 965075001 * q^58 - 447530919 * q^59 + 252903315 * q^60 + 779914845 * q^61 + 280216443 * q^62 - 417625320 * q^63 - 1134480297 * q^64 + 687619191 * q^65 + 1855998015 * q^66 + 1247609985 * q^67 - 1882788537 * q^68 - 2772677793 * q^69 - 358585647 * q^70 + 1371455385 * q^71 + 3678039405 * q^72 + 2028395037 * q^73 + 190734795 * q^74 - 1846394817 * q^75 - 4225654713 * q^76 - 1818829152 * q^77 - 1970470887 * q^78 + 2037885933 * q^79 + 2286631260 * q^80 + 7316023071 * q^81 + 7567810488 * q^82 + 1804161555 * q^83 - 11327969898 * q^84 - 4578039183 * q^85 - 4459116846 * q^86 - 2354038665 * q^87 + 1036719324 * q^88 - 1551222663 * q^89 + 19228857738 * q^90 + 5117686707 * q^91 + 9723420978 * q^92 + 4909387041 * q^93 - 4493958024 * q^94 - 3688032783 * q^95 - 21565252254 * q^96 - 4615571394 * q^97 - 22074309852 * q^98 - 5220694956 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.10.a	\(\chi_{49}(1, \cdot)\)	49.10.a.a	1	1
		49.10.a.b	2
		49.10.a.c	3
		49.10.a.d	4
		49.10.a.e	5
		49.10.a.f	5
		49.10.a.g	8
49.10.c	\(\chi_{49}(18, \cdot)\)	49.10.c.a	2	2
		49.10.c.b	4
		49.10.c.c	4
		49.10.c.d	6
		49.10.c.e	6
		49.10.c.f	8
		49.10.c.g	10
		49.10.c.h	16
49.10.e	\(\chi_{49}(8, \cdot)\)	49.10.e.a	246	6
49.10.g	\(\chi_{49}(2, \cdot)\)	49.10.g.a	492	12

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)