Space of modular forms of level 15 and weight 6

• Label: 15.6
• Level: 15
• Weight: 6
• Dimension: 24
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 96
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	48	32	16
Cusp forms	32	24	8
Eisenstein series	16	8	8

Trace form

24 * q + 4 * q^2 - 18 * q^3 + 88 * q^4 + 120 * q^5 - 156 * q^6 - 312 * q^7 - 228 * q^8 + 1800 * q^10 + 1168 * q^11 - 444 * q^12 - 2904 * q^13 - 5976 * q^14 - 3450 * q^15 + 4720 * q^16 + 2656 * q^17 + 6324 * q^18 + 3376 * q^19 + 2540 * q^20 + 1776 * q^21 - 3448 * q^22 + 264 * q^23 + 3888 * q^24 + 6360 * q^25 + 1576 * q^26 - 14418 * q^27 - 11624 * q^28 + 5072 * q^29 - 20040 * q^30 - 40608 * q^31 - 27052 * q^32 + 288 * q^33 + 8296 * q^34 + 21560 * q^35 + 75864 * q^36 + 70728 * q^37 + 56104 * q^38 + 12852 * q^39 - 1880 * q^40 - 14800 * q^41 - 75696 * q^42 - 71880 * q^43 - 77320 * q^44 - 30960 * q^45 - 92088 * q^46 - 1160 * q^47 + 25140 * q^48 + 13264 * q^49 + 55900 * q^50 + 143820 * q^51 + 265296 * q^52 + 19744 * q^53 + 20412 * q^54 + 90800 * q^55 - 68160 * q^56 - 144576 * q^57 - 206952 * q^58 - 106496 * q^59 - 331320 * q^60 - 239184 * q^61 - 19704 * q^62 + 124248 * q^63 + 176840 * q^64 + 138160 * q^65 + 238848 * q^66 + 108456 * q^67 + 240728 * q^68 + 161784 * q^69 + 202920 * q^70 - 111184 * q^71 - 347148 * q^72 - 178536 * q^73 - 222496 * q^74 - 211170 * q^75 - 211408 * q^76 + 29856 * q^77 + 330744 * q^78 + 217840 * q^79 + 171500 * q^80 + 378504 * q^81 + 393896 * q^82 + 20952 * q^83 + 203616 * q^84 - 86760 * q^85 - 58832 * q^86 - 388092 * q^87 - 642168 * q^88 - 293664 * q^89 - 432600 * q^90 - 549168 * q^91 - 169632 * q^92 - 163008 * q^93 - 425768 * q^94 + 135760 * q^95 + 563568 * q^96 + 525576 * q^97 + 236084 * q^98 + 40176 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)

We only show spaces with even 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
15.6.a	\(\chi_{15}(1, \cdot)\)	15.6.a.a	1	1
		15.6.a.b	1
		15.6.a.c	2
15.6.b	\(\chi_{15}(4, \cdot)\)	15.6.b.a	4	1
15.6.e	\(\chi_{15}(2, \cdot)\)	15.6.e.a	16	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)