Space of modular forms of level 40 and weight 5

• Label: 40.5
• Level: 40
• Weight: 5
• Dimension: 94
• Nonzero newspaces: 4
• Newform subspaces: 8
• Sturm bound: 480
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(40))\).

	Total	New	Old
Modular forms	216	106	110
Cusp forms	168	94	74
Eisenstein series	48	12	36

Trace form

94 * q - 8 * q^2 + 20 * q^4 + 24 * q^5 + 128 * q^6 - 84 * q^7 - 308 * q^8 - 58 * q^9 - 244 * q^10 + 332 * q^11 + 456 * q^12 + 20 * q^13 + 1136 * q^14 + 524 * q^15 + 40 * q^16 + 176 * q^17 - 124 * q^18 - 1412 * q^19 - 304 * q^20 - 208 * q^21 - 1840 * q^22 - 1924 * q^23 - 2488 * q^24 - 3178 * q^25 + 136 * q^26 + 3408 * q^27 + 1800 * q^28 + 4080 * q^30 + 664 * q^31 - 248 * q^32 + 3888 * q^33 - 1388 * q^34 + 3788 * q^35 - 12256 * q^36 + 3580 * q^37 - 5104 * q^38 + 6036 * q^40 - 7788 * q^41 + 14496 * q^42 + 3168 * q^43 + 7808 * q^44 - 9596 * q^45 - 3184 * q^46 - 14404 * q^47 + 520 * q^48 + 946 * q^49 - 2204 * q^50 - 1440 * q^51 + 916 * q^52 + 12060 * q^53 + 17176 * q^54 + 19888 * q^55 + 5776 * q^56 + 22840 * q^57 + 236 * q^58 + 20540 * q^59 - 3240 * q^60 - 8208 * q^61 - 1504 * q^62 - 22396 * q^63 - 14560 * q^64 - 33116 * q^65 - 22928 * q^66 - 36480 * q^67 + 660 * q^68 - 23640 * q^70 - 17192 * q^71 - 34028 * q^72 + 33336 * q^73 - 22084 * q^74 + 23024 * q^75 - 3536 * q^76 + 10320 * q^77 - 3656 * q^78 - 4584 * q^80 - 23754 * q^81 - 1524 * q^82 - 25680 * q^83 + 16480 * q^84 - 36588 * q^85 + 49904 * q^86 + 39992 * q^87 + 77120 * q^88 - 1972 * q^89 + 103196 * q^90 + 84920 * q^91 + 55440 * q^92 + 53040 * q^93 + 3976 * q^94 + 8008 * q^95 + 47632 * q^96 + 25784 * q^97 - 42064 * q^98 - 46596 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(40))\)

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
40.5.b	\(\chi_{40}(31, \cdot)\)	None	0	1
40.5.e	\(\chi_{40}(19, \cdot)\)	40.5.e.a	1	1
		40.5.e.b	1
		40.5.e.c	20
40.5.g	\(\chi_{40}(11, \cdot)\)	40.5.g.a	16	1
40.5.h	\(\chi_{40}(39, \cdot)\)	None	0	1
40.5.i	\(\chi_{40}(13, \cdot)\)	40.5.i.a	44	2
40.5.l	\(\chi_{40}(17, \cdot)\)	40.5.l.a	2	2
		40.5.l.b	4
		40.5.l.c	6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(40))\) into lower level spaces

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