Space of modular forms of level 15 and weight 5

• Label: 15.5
• Level: 15
• Weight: 5
• Dimension: 20
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 80
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(80\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	40	24	16
Cusp forms	24	20	4
Eisenstein series	16	4	12

Trace form

20 * q + 8 * q^3 - 8 * q^4 - 84 * q^5 - 32 * q^6 + 96 * q^7 + 180 * q^8 + 136 * q^9 - 116 * q^10 - 288 * q^11 - 812 * q^12 - 764 * q^13 + 764 * q^15 + 1536 * q^16 + 900 * q^17 + 1160 * q^18 + 512 * q^19 + 564 * q^20 + 384 * q^21 - 760 * q^22 - 1560 * q^23 - 4248 * q^24 - 2884 * q^25 - 3024 * q^26 - 352 * q^27 - 184 * q^28 + 1876 * q^30 - 448 * q^31 + 4980 * q^32 + 7120 * q^33 + 11992 * q^34 + 6600 * q^35 + 1088 * q^36 - 1924 * q^37 - 7680 * q^38 - 8824 * q^39 - 15312 * q^40 - 2712 * q^41 - 9360 * q^42 - 8624 * q^43 + 6976 * q^45 + 15112 * q^46 + 4800 * q^47 + 18268 * q^48 + 12152 * q^49 + 3744 * q^50 - 3824 * q^51 + 7736 * q^52 + 1020 * q^53 - 19664 * q^54 - 14304 * q^55 - 30720 * q^56 - 16984 * q^57 - 21400 * q^58 + 18136 * q^60 + 10944 * q^61 + 28680 * q^62 + 15336 * q^63 + 13704 * q^64 - 1212 * q^65 + 6608 * q^66 + 4896 * q^67 - 1920 * q^68 - 624 * q^69 + 600 * q^70 + 7536 * q^71 - 6900 * q^72 + 12196 * q^73 + 2384 * q^75 + 2592 * q^76 - 360 * q^77 - 6080 * q^78 - 21848 * q^79 + 10644 * q^80 - 3500 * q^81 - 58440 * q^82 - 32400 * q^83 - 17544 * q^84 - 30788 * q^85 + 14592 * q^86 + 5720 * q^87 + 1320 * q^88 - 14716 * q^90 + 19872 * q^91 - 31800 * q^92 + 5856 * q^93 + 63112 * q^94 + 18864 * q^95 + 19808 * q^96 + 68396 * q^97 + 46440 * q^98 + 37760 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.5.c	\(\chi_{15}(11, \cdot)\)	15.5.c.a	6	1
15.5.d	\(\chi_{15}(14, \cdot)\)	15.5.d.a	1	1
		15.5.d.b	1
		15.5.d.c	4
15.5.f	\(\chi_{15}(7, \cdot)\)	15.5.f.a	8	2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

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