Space of modular forms of level 10 and weight 5

• Label: 10.5
• Level: 10
• Weight: 5
• Dimension: 4
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 30
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(10))\).

	Total	New	Old
Modular forms	16	4	12
Cusp forms	8	4	4
Eisenstein series	8	0	8

Trace form

4 * q + 20 * q^3 - 60 * q^5 - 64 * q^6 + 20 * q^7 + 160 * q^10 + 168 * q^11 + 160 * q^12 - 60 * q^13 + 20 * q^15 - 256 * q^16 - 1020 * q^17 - 640 * q^18 + 968 * q^21 + 1280 * q^22 + 1620 * q^23 - 700 * q^25 - 1344 * q^26 + 320 * q^27 - 160 * q^28 + 960 * q^30 - 1112 * q^31 - 1720 * q^33 - 2220 * q^35 + 32 * q^36 - 1020 * q^37 + 960 * q^38 + 1280 * q^40 + 5448 * q^41 - 2240 * q^42 + 660 * q^43 + 6400 * q^45 + 2176 * q^46 + 1620 * q^47 - 1280 * q^48 - 4800 * q^50 - 10712 * q^51 - 480 * q^52 - 4860 * q^53 - 2520 * q^55 + 3072 * q^56 + 5120 * q^57 + 3520 * q^58 - 4960 * q^60 - 7032 * q^61 - 3840 * q^62 + 7700 * q^63 + 7620 * q^65 + 10112 * q^66 + 8660 * q^67 + 8160 * q^68 + 1600 * q^70 + 5928 * q^71 - 5120 * q^72 - 12860 * q^73 - 13100 * q^75 - 5120 * q^76 - 14520 * q^77 - 5760 * q^78 + 3840 * q^80 + 964 * q^81 - 2560 * q^82 - 300 * q^83 + 16580 * q^85 - 14784 * q^86 + 11840 * q^87 - 10240 * q^88 + 9440 * q^90 + 15528 * q^91 + 12960 * q^92 + 2120 * q^93 - 9600 * q^95 + 4096 * q^96 - 13500 * q^97 + 3840 * q^98

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)

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
10.5.c	\(\chi_{10}(3, \cdot)\)	10.5.c.a	2	2
		10.5.c.b	2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 1}\)