Space of modular forms of level 48 and weight 14

• Label: 48.14
• Level: 48
• Weight: 14
• Dimension: 347
• Nonzero newspaces: 4
• Sturm bound: 1792
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(1792\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(48))\).

	Total	New	Old
Modular forms	860	355	505
Cusp forms	804	347	457
Eisenstein series	56	8	48

Trace form

347 * q + 727 * q^3 - 728 * q^4 - 33802 * q^5 + 255052 * q^6 - 182888 * q^7 + 2153748 * q^8 + 7890447 * q^9 - 3619616 * q^10 + 14171988 * q^11 + 36466552 * q^12 + 498878 * q^13 + 64418244 * q^14 - 113906250 * q^15 - 19761584 * q^16 - 49714598 * q^17 - 141658160 * q^18 - 968193136 * q^19 + 175250000 * q^20 - 1016215532 * q^21 - 997973192 * q^22 + 468181576 * q^23 - 2544744852 * q^24 - 5198599035 * q^25 + 6587555020 * q^26 + 2459308915 * q^27 - 8592554880 * q^28 + 6777442990 * q^29 - 16913856740 * q^30 + 18875263408 * q^31 + 28752946560 * q^32 + 7402550792 * q^33 - 78459185528 * q^34 - 34494297576 * q^35 + 72143738768 * q^36 + 33331987814 * q^37 - 41340751768 * q^38 - 128312805742 * q^39 - 160253901624 * q^40 + 26590174098 * q^41 + 120990123756 * q^42 + 13016810976 * q^43 - 199004849672 * q^44 - 48043128342 * q^45 - 1880998272 * q^46 - 64231873344 * q^47 - 171654023904 * q^48 + 925880630343 * q^49 - 676218619548 * q^50 - 87819625518 * q^51 + 1194444782320 * q^52 - 555914273018 * q^53 - 1134089731276 * q^54 + 341388695840 * q^55 + 417469643136 * q^56 - 588989127720 * q^57 + 1056098938696 * q^58 - 274339758340 * q^59 - 2349582560104 * q^60 - 1887170236866 * q^61 - 1258171890180 * q^62 + 402998087592 * q^63 + 2245613690944 * q^64 + 731443949796 * q^65 + 1028460170572 * q^66 + 82196616688 * q^67 - 7648944940256 * q^68 - 1055828032868 * q^69 + 11094525732888 * q^70 - 2503040468680 * q^71 + 5001438425188 * q^72 - 4035141495642 * q^73 - 12005887333012 * q^74 + 4624908130469 * q^75 - 3481883108048 * q^76 + 7080631693904 * q^77 + 11183573869464 * q^78 - 23257046585584 * q^79 - 6673966167032 * q^80 - 23030710984021 * q^81 - 3887414161128 * q^82 + 25121786396220 * q^83 - 9511267559144 * q^84 + 1167979073724 * q^85 + 7504403958736 * q^86 - 32315340712662 * q^87 - 21060864794816 * q^88 + 3266332491858 * q^89 + 39867512334392 * q^90 + 51025537603328 * q^91 + 9188451742768 * q^92 - 1364691088256 * q^93 - 5205964821304 * q^94 - 104701294901176 * q^95 - 19876149541496 * q^96 - 23266745243866 * q^97 - 29583132758744 * q^98 + 29280615671072 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(48))\)

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
48.14.a	\(\chi_{48}(1, \cdot)\)	48.14.a.a	1	1
		48.14.a.b	1
		48.14.a.c	1
		48.14.a.d	1
		48.14.a.e	1
		48.14.a.f	2
		48.14.a.g	2
		48.14.a.h	2
		48.14.a.i	2
48.14.c	\(\chi_{48}(47, \cdot)\)	48.14.c.a	2	1
		48.14.c.b	8
		48.14.c.c	16
48.14.d	\(\chi_{48}(25, \cdot)\)	None	0	1
48.14.f	\(\chi_{48}(23, \cdot)\)	None	0	1
48.14.j	\(\chi_{48}(13, \cdot)\)	n/a	104	2
48.14.k	\(\chi_{48}(11, \cdot)\)	n/a	204	2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(48))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(48)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)