Space of modular forms of level 49 and weight 5

• Label: 49.5
• Level: 49
• Weight: 5
• Dimension: 352
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 980
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 49 = 7^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(980\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(49))\).

	Total	New	Old
Modular forms	422	400	22
Cusp forms	362	352	10
Eisenstein series	60	48	12

Trace form

352 * q - 15 * q^2 - 33 * q^3 + 49 * q^4 + 39 * q^5 - 21 * q^6 - 70 * q^7 - 585 * q^8 - 135 * q^9 + 387 * q^10 + 507 * q^11 + 1155 * q^12 - 21 * q^13 - 630 * q^14 - 975 * q^15 - 295 * q^16 + 471 * q^17 - 615 * q^18 - 1305 * q^19 - 21 * q^20 + 1029 * q^21 + 2901 * q^22 + 867 * q^23 - 1461 * q^24 - 127 * q^25 - 2037 * q^26 - 21 * q^27 + 742 * q^28 + 1845 * q^29 + 123 * q^30 - 7257 * q^31 - 4599 * q^32 - 4161 * q^33 - 21 * q^34 + 2457 * q^35 + 17319 * q^36 + 17583 * q^37 + 22395 * q^38 + 4158 * q^39 - 12645 * q^40 - 9723 * q^41 - 30261 * q^42 - 17125 * q^43 - 47313 * q^44 - 29424 * q^45 - 25497 * q^46 - 843 * q^47 + 6706 * q^49 - 318 * q^50 + 32883 * q^51 + 60571 * q^52 + 37173 * q^53 + 76443 * q^54 + 44814 * q^55 + 51114 * q^56 - 9669 * q^57 + 12759 * q^58 - 6459 * q^59 - 34797 * q^60 - 29396 * q^61 - 42357 * q^62 - 45234 * q^63 - 20681 * q^64 - 11613 * q^65 + 5091 * q^66 - 7277 * q^67 - 40845 * q^68 - 21 * q^69 - 3381 * q^70 + 14949 * q^71 + 7593 * q^72 - 10449 * q^73 - 5505 * q^74 + 19251 * q^75 - 21 * q^76 + 18963 * q^77 + 41433 * q^78 + 23491 * q^79 + 144426 * q^80 + 94581 * q^81 + 104118 * q^82 + 35259 * q^83 + 2394 * q^84 + 4737 * q^85 - 107676 * q^86 - 136293 * q^87 - 204474 * q^88 - 144609 * q^89 - 365904 * q^90 - 91245 * q^91 - 98460 * q^92 - 186273 * q^93 - 157050 * q^94 - 75633 * q^95 - 67872 * q^96 + 92736 * q^98 + 77760 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.5.b	\(\chi_{49}(48, \cdot)\)	49.5.b.a	4	1
		49.5.b.b	8
49.5.d	\(\chi_{49}(19, \cdot)\)	49.5.d.a	2	2
		49.5.d.b	4
		49.5.d.c	16
49.5.f	\(\chi_{49}(6, \cdot)\)	49.5.f.a	102	6
49.5.h	\(\chi_{49}(3, \cdot)\)	49.5.h.a	216	12

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

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