Space of modular forms of level 16 and weight 8

• Label: 16.8
• Level: 16
• Weight: 8
• Dimension: 29
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 128
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 16 = 2^{4} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(16))\).

	Total	New	Old
Modular forms	63	34	29
Cusp forms	49	29	20
Eisenstein series	14	5	9

Trace form

29 * q - 2 * q^2 + 26 * q^3 - 184 * q^4 + 136 * q^5 - 176 * q^6 + 664 * q^7 - 1004 * q^8 + 2575 * q^9 + 12972 * q^10 + 5798 * q^11 - 27356 * q^12 - 3280 * q^13 + 22268 * q^14 - 50292 * q^15 + 13336 * q^16 - 12718 * q^17 - 29346 * q^18 + 101874 * q^19 + 46204 * q^20 + 1012 * q^21 - 44348 * q^22 - 151992 * q^23 - 59216 * q^24 + 1349 * q^25 - 35960 * q^26 + 149648 * q^27 + 220312 * q^28 + 68376 * q^29 + 27636 * q^30 - 80944 * q^31 - 248632 * q^32 + 85900 * q^33 + 924660 * q^34 + 450284 * q^35 - 1015508 * q^36 + 104320 * q^37 - 5472 * q^38 - 1191128 * q^39 - 1121976 * q^40 - 167154 * q^41 + 124600 * q^42 + 1180142 * q^43 - 758620 * q^44 + 73716 * q^45 + 2335660 * q^46 - 2151200 * q^47 + 4141288 * q^48 - 1379351 * q^49 - 787194 * q^50 + 2212316 * q^51 + 410324 * q^52 + 1522976 * q^53 - 7404512 * q^54 + 1382872 * q^55 - 4093160 * q^56 - 1066640 * q^57 - 1860712 * q^58 - 5642226 * q^59 + 5147328 * q^60 + 4110448 * q^61 + 6274096 * q^62 + 12283836 * q^63 + 10452224 * q^64 + 1797424 * q^65 + 10937812 * q^66 - 13064014 * q^67 - 7403760 * q^68 - 10755324 * q^69 - 22140800 * q^70 + 6673752 * q^71 - 25293948 * q^72 - 6370898 * q^73 - 13177044 * q^74 - 4074918 * q^75 + 17814260 * q^76 + 13737460 * q^77 + 37993916 * q^78 - 4946000 * q^79 + 40047272 * q^80 + 2649165 * q^81 + 22858240 * q^82 + 5807626 * q^83 - 30159704 * q^84 - 1792312 * q^85 - 54129468 * q^86 + 4209000 * q^87 - 59216392 * q^88 - 6818562 * q^89 - 33515304 * q^90 + 3757204 * q^91 + 21810936 * q^92 + 2686640 * q^93 + 77196112 * q^94 - 10595172 * q^95 + 116940464 * q^96 + 13548002 * q^97 + 21823866 * q^98 + 32541154 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.8.a	\(\chi_{16}(1, \cdot)\)	16.8.a.a	1	1
		16.8.a.b	1
		16.8.a.c	1
16.8.b	\(\chi_{16}(9, \cdot)\)	None	0	1
16.8.e	\(\chi_{16}(5, \cdot)\)	16.8.e.a	26	2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)