Space of modular forms of level 40 and weight 11

• Label: 40.11
• Level: 40
• Weight: 11
• Dimension: 244
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 1056
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 11 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(1056\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(40))\).

	Total	New	Old
Modular forms	504	256	248
Cusp forms	456	244	212
Eisenstein series	48	12	36

Trace form

244 * q - 24 * q^2 - 2476 * q^4 - 3116 * q^5 - 20032 * q^6 - 18396 * q^7 + 65676 * q^8 - 275566 * q^9 - 9124 * q^10 - 107852 * q^11 + 390696 * q^12 + 461282 * q^13 - 1191664 * q^14 + 1413524 * q^15 + 4800424 * q^16 - 2490866 * q^17 - 6663148 * q^18 - 10214084 * q^19 + 10407376 * q^20 + 2089880 * q^21 - 11962768 * q^22 - 9951268 * q^23 - 34349080 * q^24 - 91853008 * q^25 + 45362792 * q^26 + 114497016 * q^27 - 82567512 * q^28 - 54779280 * q^30 - 157402328 * q^31 + 252262856 * q^32 + 157809816 * q^33 + 18975220 * q^34 + 116290868 * q^35 - 264024160 * q^36 - 197979002 * q^37 - 273590768 * q^38 - 104546604 * q^40 + 299377860 * q^41 + 553900416 * q^42 - 578319408 * q^43 - 763203584 * q^44 - 407479646 * q^45 - 1050760048 * q^46 + 999294780 * q^47 + 1776097384 * q^48 - 404086010 * q^49 - 128146444 * q^50 - 89833968 * q^51 - 685002092 * q^52 + 707661654 * q^53 - 6146111048 * q^54 - 312870872 * q^55 + 2064307792 * q^56 - 225349544 * q^57 + 3958508108 * q^58 + 89196828 * q^59 - 1612554120 * q^60 - 2230704120 * q^61 - 1432033984 * q^62 + 4367917796 * q^63 + 7357423904 * q^64 + 1314782054 * q^65 + 6928565872 * q^66 + 2552886144 * q^67 - 11913010764 * q^68 - 4311078360 * q^70 - 1873072568 * q^71 + 15712287796 * q^72 - 2770272318 * q^73 + 4062189756 * q^74 + 7457343464 * q^75 + 3161423920 * q^76 + 7179019752 * q^77 - 756690248 * q^78 - 1340058184 * q^80 - 17202124272 * q^81 - 4646920596 * q^82 - 12926174584 * q^83 - 3448190240 * q^84 + 4646506242 * q^85 - 14656799504 * q^86 + 26646475352 * q^87 + 9621098816 * q^88 - 8019871484 * q^89 + 33289416236 * q^90 - 9869625448 * q^91 + 3449071952 * q^92 - 8283146280 * q^93 - 15475271864 * q^94 - 1638074992 * q^95 - 75013318832 * q^96 + 27302694434 * q^97 - 86273852512 * q^98 + 33162199548 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(40))\)

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
40.11.b	\(\chi_{40}(31, \cdot)\)	None	0	1
40.11.e	\(\chi_{40}(19, \cdot)\)	40.11.e.a	1	1
		40.11.e.b	1
		40.11.e.c	56
40.11.g	\(\chi_{40}(11, \cdot)\)	40.11.g.a	40	1
40.11.h	\(\chi_{40}(39, \cdot)\)	None	0	1
40.11.i	\(\chi_{40}(13, \cdot)\)	40.11.i.a	116	2
40.11.l	\(\chi_{40}(17, \cdot)\)	40.11.l.a	14	2
		40.11.l.b	16

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(40))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(40)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)