Space of modular forms of level 56 and weight 5

• Label: 56.5
• Level: 56
• Weight: 5
• Dimension: 198
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 960
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(960\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(56))\).

	Total	New	Old
Modular forms	420	218	202
Cusp forms	348	198	150
Eisenstein series	72	20	52

Trace form

198 * q - 10 * q^2 - 2 * q^3 + 18 * q^4 + 130 * q^6 - 6 * q^7 - 316 * q^8 - 110 * q^9 - 486 * q^10 - 26 * q^11 + 778 * q^12 + 474 * q^14 + 612 * q^15 - 1062 * q^16 + 664 * q^17 - 1592 * q^18 - 2586 * q^19 - 180 * q^20 - 840 * q^21 + 3102 * q^22 + 2154 * q^23 + 4942 * q^24 + 1734 * q^25 + 2004 * q^26 + 3964 * q^27 - 3606 * q^28 - 10230 * q^30 - 2142 * q^31 - 4000 * q^32 - 4108 * q^33 + 702 * q^34 - 8382 * q^35 - 3782 * q^36 - 1224 * q^37 + 5968 * q^38 + 1596 * q^39 + 9504 * q^40 - 1496 * q^41 + 10650 * q^42 + 8136 * q^43 + 8722 * q^44 + 5304 * q^45 - 7776 * q^46 + 14898 * q^47 - 15842 * q^48 + 3222 * q^49 - 22102 * q^50 - 502 * q^51 - 16356 * q^52 - 1800 * q^53 - 8306 * q^54 - 1104 * q^56 + 5312 * q^57 + 8292 * q^58 - 1202 * q^59 + 45168 * q^60 - 17640 * q^61 + 47544 * q^62 - 42726 * q^63 + 10458 * q^64 - 17460 * q^65 - 6298 * q^66 - 35394 * q^67 - 21902 * q^68 - 44862 * q^70 + 24324 * q^71 - 14684 * q^72 - 5328 * q^73 + 23286 * q^74 + 82852 * q^75 + 45522 * q^76 + 38448 * q^77 + 57888 * q^78 + 37770 * q^79 + 24756 * q^80 + 35506 * q^81 + 25674 * q^82 - 13448 * q^83 - 23802 * q^84 - 35952 * q^85 - 32330 * q^86 - 67608 * q^87 - 43902 * q^88 + 2944 * q^89 - 75168 * q^90 - 31920 * q^91 - 48102 * q^92 - 70344 * q^93 - 23898 * q^94 - 726 * q^95 + 56674 * q^96 - 16344 * q^97 - 3322 * q^98 + 19040 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(56))\)

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
56.5.c	\(\chi_{56}(41, \cdot)\)	56.5.c.a	8	1
56.5.d	\(\chi_{56}(15, \cdot)\)	None	0	1
56.5.g	\(\chi_{56}(43, \cdot)\)	56.5.g.a	2	1
		56.5.g.b	22
56.5.h	\(\chi_{56}(13, \cdot)\)	56.5.h.a	1	1
		56.5.h.b	1
		56.5.h.c	2
		56.5.h.d	2
		56.5.h.e	24
56.5.j	\(\chi_{56}(5, \cdot)\)	56.5.j.a	60	2
56.5.k	\(\chi_{56}(11, \cdot)\)	56.5.k.a	60	2
56.5.n	\(\chi_{56}(23, \cdot)\)	None	0	2
56.5.o	\(\chi_{56}(17, \cdot)\)	56.5.o.a	16	2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(56))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(56)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)