Space of modular forms of level 24 and weight 14

• Label: 24.14
• Level: 24
• Weight: 14
• Dimension: 83
• Nonzero newspaces: 3
• Newform subspaces: 7
• Sturm bound: 448
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(24))\).

	Total	New	Old
Modular forms	220	87	133
Cusp forms	196	83	113
Eisenstein series	24	4	20

Trace form

83 * q + 2 * q^2 - 731 * q^3 + 17108 * q^4 - 59542 * q^5 - 42062 * q^6 - 441532 * q^7 - 1126012 * q^8 - 10097381 * q^9 + 11668420 * q^10 - 4960588 * q^11 - 731048 * q^12 - 5909102 * q^13 + 7518380 * q^14 + 63567342 * q^15 - 50555616 * q^16 + 275168810 * q^17 + 240623254 * q^18 + 100840944 * q^19 - 378367336 * q^20 + 396021960 * q^21 - 641662112 * q^22 + 14821776 * q^23 - 2471875964 * q^24 + 8237477481 * q^25 + 5510708936 * q^26 + 1684467937 * q^27 - 14837401872 * q^28 + 5020606866 * q^29 + 24625282788 * q^30 + 13987106484 * q^31 - 17566199288 * q^32 - 6737644468 * q^33 + 19062948908 * q^34 + 32209870896 * q^35 + 42205623772 * q^36 - 3896179782 * q^37 + 7007079448 * q^38 - 100151478 * q^39 + 62483736296 * q^40 - 4518920806 * q^41 + 8440723908 * q^42 + 85217200832 * q^43 + 66382564608 * q^44 - 31643060022 * q^45 + 187013263816 * q^46 + 128799019032 * q^47 - 12038793416 * q^48 - 22975225121 * q^49 - 466066267486 * q^50 + 269122604942 * q^51 - 414909890192 * q^52 + 15885311834 * q^53 - 200931909458 * q^54 - 595424069576 * q^55 + 831087057464 * q^56 + 195367911584 * q^57 - 1829286161868 * q^58 - 1137562112668 * q^59 - 909072932112 * q^60 + 243378052738 * q^61 + 1603424829460 * q^62 + 265539810060 * q^63 - 561977463952 * q^64 + 702147820732 * q^65 + 907630416296 * q^66 - 5238874392840 * q^67 - 4312601747136 * q^68 + 130938250248 * q^69 + 5487308708248 * q^70 + 9383663088112 * q^71 + 1595942808460 * q^72 - 3137625658450 * q^73 - 10599806748688 * q^74 - 6510318188237 * q^75 - 10158554183640 * q^76 - 464077787040 * q^77 + 9362727069480 * q^78 + 8997668156244 * q^79 + 12853624265856 * q^80 + 8041897439203 * q^81 - 11344356038076 * q^82 - 3303049206164 * q^83 - 3693317594184 * q^84 + 447599113652 * q^85 + 17294271264872 * q^86 - 620690296122 * q^87 + 50918802903472 * q^88 - 3797011335214 * q^89 - 17803341395604 * q^90 - 8572643746512 * q^91 - 26294566253184 * q^92 + 6963083635824 * q^93 + 29516333563848 * q^94 + 27514418670584 * q^95 + 15050986307800 * q^96 + 28934476608614 * q^97 - 68853694633926 * q^98 + 29280243662372 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.14.a	\(\chi_{24}(1, \cdot)\)	24.14.a.a	1	1
		24.14.a.b	2
		24.14.a.c	2
		24.14.a.d	2
24.14.c	\(\chi_{24}(23, \cdot)\)	None	0	1
24.14.d	\(\chi_{24}(13, \cdot)\)	24.14.d.a	26	1
24.14.f	\(\chi_{24}(11, \cdot)\)	24.14.f.a	2	1
		24.14.f.b	48

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

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