Space of modular forms of level 24 and weight 13

• Label: 24.13
• Level: 24
• Weight: 13
• Dimension: 82
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 416
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	=	\( 13 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(416\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(\Gamma_1(24))\).

	Total	New	Old
Modular forms	204	86	118
Cusp forms	180	82	98
Eisenstein series	24	4	20

Trace form

82 * q + 90 * q^2 - 460 * q^3 - 3308 * q^4 + 80482 * q^6 - 198844 * q^7 - 308340 * q^8 + 4091954 * q^9 - 1326412 * q^10 + 5336640 * q^11 - 5856800 * q^12 - 3855720 * q^13 - 4099932 * q^14 - 5824068 * q^15 - 6163808 * q^16 + 4839120 * q^17 - 53429290 * q^18 + 22213608 * q^19 + 172894248 * q^20 - 20608296 * q^21 - 71789824 * q^22 + 248019068 * q^24 + 26326158 * q^25 - 429245136 * q^26 - 917401420 * q^27 + 1133287376 * q^28 + 367439588 * q^30 - 1921290748 * q^31 - 285053400 * q^32 - 1867710484 * q^33 + 5812895340 * q^34 + 6653503296 * q^35 - 6122949972 * q^36 - 2937811560 * q^37 + 9895366440 * q^38 - 9733890168 * q^39 - 5401693096 * q^40 + 4610651760 * q^41 - 7089029204 * q^42 - 33092921880 * q^43 + 19440004032 * q^44 + 238752832 * q^45 + 58510465560 * q^46 - 57178141320 * q^48 + 53820692934 * q^49 + 3733112754 * q^50 + 61636672 * q^51 + 18014578560 * q^52 - 53322532282 * q^54 + 89838393976 * q^55 - 101048807592 * q^56 + 4198723560 * q^57 - 286292276284 * q^58 - 3525080832 * q^59 + 139383239088 * q^60 + 85151585304 * q^61 + 346538979180 * q^62 - 61419017084 * q^63 - 296481711248 * q^64 - 191993909184 * q^65 - 132692562600 * q^66 - 218594933400 * q^67 + 746141861520 * q^68 + 42989010368 * q^69 + 542121204808 * q^70 + 232881136340 * q^72 - 359264483164 * q^73 - 895761013320 * q^74 - 484421370188 * q^75 + 1353964688280 * q^76 + 779153084720 * q^78 - 35437906300 * q^79 - 2394665516448 * q^80 + 1363978669650 * q^81 - 2219540460780 * q^82 - 686759112000 * q^83 + 929511679576 * q^84 - 504880721664 * q^85 + 2793739306968 * q^86 + 1005529700796 * q^87 - 2831325868144 * q^88 + 506630638800 * q^89 + 41539474028 * q^90 - 1016601775536 * q^91 + 1830106686240 * q^92 + 70819872280 * q^93 + 4319873854680 * q^94 - 2034883114984 * q^96 - 455933853724 * q^97 - 3395057076990 * q^98 + 192147032320 * q^99

Decomposition of \(S_{13}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.13.b	\(\chi_{24}(19, \cdot)\)	24.13.b.a	24	1
24.13.e	\(\chi_{24}(17, \cdot)\)	24.13.e.a	12	1
24.13.g	\(\chi_{24}(7, \cdot)\)	None	0	1
24.13.h	\(\chi_{24}(5, \cdot)\)	24.13.h.a	1	1
		24.13.h.b	1
		24.13.h.c	44

Decomposition of \(S_{13}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{13}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{13}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{13}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)