Space of modular forms of level 15 and weight 8

• Label: 15.8
• Level: 15
• Weight: 8
• Dimension: 36
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 128
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(15))\).

	Total	New	Old
Modular forms	64	44	20
Cusp forms	48	36	12
Eisenstein series	16	8	8

Trace form

36 * q - 28 * q^2 + 78 * q^3 - 200 * q^4 - 444 * q^5 + 1356 * q^6 + 3608 * q^7 - 2436 * q^8 - 2916 * q^9 - 4616 * q^10 + 7952 * q^11 + 8340 * q^12 + 5360 * q^13 - 34488 * q^14 + 26814 * q^15 + 38000 * q^16 - 32032 * q^17 - 126972 * q^18 - 64176 * q^19 + 46444 * q^20 + 134904 * q^21 + 146376 * q^22 + 170088 * q^23 - 237168 * q^24 - 85644 * q^25 - 445816 * q^26 - 224802 * q^27 + 436280 * q^28 + 717688 * q^29 + 774336 * q^30 + 71568 * q^31 - 1063916 * q^32 - 774984 * q^33 + 238760 * q^34 + 636520 * q^35 + 569016 * q^36 - 789232 * q^37 - 769432 * q^38 - 1224396 * q^39 - 2054392 * q^40 + 883240 * q^41 + 1622112 * q^42 + 976328 * q^43 + 537976 * q^44 + 893916 * q^45 + 4371848 * q^46 + 1210520 * q^47 + 1149684 * q^48 - 2687956 * q^49 - 5555236 * q^50 - 4088820 * q^51 - 8572528 * q^52 + 1575488 * q^53 - 393660 * q^54 + 7062576 * q^55 + 6479040 * q^56 + 5320296 * q^57 - 1200264 * q^58 - 1197184 * q^59 + 6515256 * q^60 + 1179144 * q^61 + 5573928 * q^62 - 323496 * q^63 + 9724488 * q^64 - 3366592 * q^65 - 30638208 * q^66 - 21756808 * q^67 - 9434504 * q^68 - 5890968 * q^69 - 1513560 * q^70 - 4007216 * q^71 + 34470036 * q^72 + 6676736 * q^73 + 20919712 * q^74 + 19838094 * q^75 + 37710128 * q^76 + 6733248 * q^77 - 10796952 * q^78 - 10874880 * q^79 - 39917876 * q^80 - 24912684 * q^81 - 40630392 * q^82 - 17321256 * q^83 - 43954272 * q^84 - 33002768 * q^85 - 6212848 * q^86 + 50204484 * q^87 + 97866504 * q^88 + 58210824 * q^89 + 80324424 * q^90 + 88309648 * q^91 + 15479424 * q^92 - 54464928 * q^93 - 78524776 * q^94 - 33956656 * q^95 - 104433168 * q^96 - 63625168 * q^97 - 21248492 * q^98 - 9879408 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)

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
15.8.a	\(\chi_{15}(1, \cdot)\)	15.8.a.a	1	1
		15.8.a.b	1
		15.8.a.c	2
15.8.b	\(\chi_{15}(4, \cdot)\)	15.8.b.a	8	1
15.8.e	\(\chi_{15}(2, \cdot)\)	15.8.e.a	24	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(15))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(15)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)