Space of modular forms of level 12 and weight 16

• Label: 12.16
• Level: 12
• Weight: 16
• Dimension: 31
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 128
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(12))\).

	Total	New	Old
Modular forms	65	35	30
Cusp forms	55	31	24
Eisenstein series	10	4	6

Trace form

31 * q + 2187 * q^3 + 26968 * q^4 + 115362 * q^5 + 823656 * q^6 + 3709392 * q^7 + 10536855 * q^9 - 43831600 * q^10 - 41871852 * q^11 - 226414248 * q^12 - 26296918 * q^13 + 52396146 * q^15 - 1459325408 * q^16 + 3512804742 * q^17 - 4234777584 * q^18 + 5238674700 * q^19 - 4475952456 * q^21 - 2533670160 * q^22 - 5842717992 * q^23 - 18487781856 * q^24 - 100850344911 * q^25 + 10460353203 * q^27 + 5481093840 * q^28 + 166312147338 * q^29 + 8237058960 * q^30 - 81299083368 * q^31 + 230643700980 * q^33 + 450165745472 * q^34 - 1054492684704 * q^35 + 232631927160 * q^36 + 64133965490 * q^37 + 381280158450 * q^39 + 1945471012160 * q^40 - 1220472557730 * q^41 + 1938106219632 * q^42 + 2087694689748 * q^43 - 4455341042862 * q^45 + 2270790222432 * q^46 - 4717686000672 * q^47 + 5846474725152 * q^48 - 17364113043761 * q^49 + 10933578069462 * q^51 - 6113229405424 * q^52 - 19058082641694 * q^53 + 1626598700568 * q^54 + 36285020054712 * q^55 + 37052040330756 * q^57 - 19395437098192 * q^58 - 40508760730572 * q^59 - 10924219377600 * q^60 + 9054167900330 * q^61 + 17741906944848 * q^63 + 21633892829056 * q^64 - 181772821755540 * q^65 + 4928819126448 * q^66 + 30127015867308 * q^67 + 255898488868824 * q^69 + 91772543171040 * q^70 - 271446469781400 * q^71 + 66924493142592 * q^72 + 326950045910150 * q^73 + 224850754822077 * q^75 - 205265768291280 * q^76 - 393734977656768 * q^77 + 58364283489648 * q^78 + 218426580962376 * q^79 + 184757194000719 * q^81 - 750029796726880 * q^82 - 97290581971572 * q^83 - 92605433207856 * q^84 - 75154133665724 * q^85 + 280522924065882 * q^87 - 619691835246912 * q^88 - 216695712849570 * q^89 - 471443548913520 * q^90 + 1389408878028000 * q^91 - 935248037922336 * q^93 + 1301107064491200 * q^94 + 854707412449800 * q^95 + 525428335287168 * q^96 - 2161429761173314 * q^97 - 200271770088588 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.16.a	\(\chi_{12}(1, \cdot)\)	12.16.a.a	1	1
		12.16.a.b	2
12.16.b	\(\chi_{12}(11, \cdot)\)	12.16.b.a	28	1

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)