Space of modular forms of level 24 and weight 21

• Label: 24.21
• Level: 24
• Weight: 21
• Dimension: 138
• Nonzero newspaces: 3
• Newform subspaces: 5
• Sturm bound: 672
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	=	\( 21 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(672\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(24))\).

	Total	New	Old
Modular forms	332	142	190
Cusp forms	308	138	170
Eisenstein series	24	4	20

Trace form

138 * q - 1254 * q^2 + 10604 * q^3 - 3547116 * q^4 - 27420830 * q^6 - 93663628 * q^7 + 1421873100 * q^8 + 51105443114 * q^9 - 2356735692 * q^10 + 29041257408 * q^11 + 48753367840 * q^12 + 181620533288 * q^13 + 83901599076 * q^14 + 1563397043772 * q^15 - 3982987507552 * q^16 - 1980778750800 * q^17 - 8161295071786 * q^18 - 542688462504 * q^19 + 49232945391528 * q^20 - 25495742683416 * q^21 + 161641614811392 * q^22 + 40265625355580 * q^24 + 194248063879878 * q^25 - 323770062560400 * q^26 - 93495133623700 * q^27 + 1615216562510032 * q^28 + 1559875765595108 * q^30 + 2404517102725300 * q^31 - 1295698920292824 * q^32 - 333767630309236 * q^33 + 16592920475347564 * q^34 - 6850256580373824 * q^35 - 9041925786369492 * q^36 + 5492196102407208 * q^37 + 9598100558441640 * q^38 - 25519829073856968 * q^39 - 48622249705345576 * q^40 + 10747406201475600 * q^41 - 37811045265483284 * q^42 + 55000388553672280 * q^43 + 50258899422458304 * q^44 + 27990445313547712 * q^45 - 26159709194128744 * q^46 + 98473870614975096 * q^48 + 543527051380408142 * q^49 - 273913774911892686 * q^50 - 5746109065702976 * q^51 + 34712315328604160 * q^52 + 96766581625103750 * q^54 - 942202831019412104 * q^55 + 602779869490401624 * q^56 + 74953334780063448 * q^57 + 388216756619059012 * q^58 - 1873351755117093120 * q^59 - 1945753979973352272 * q^60 + 579087271417696424 * q^61 - 172596318394979796 * q^62 - 769823852639706572 * q^63 - 5001362545597976208 * q^64 - 3150306370674383424 * q^65 - 5845350210685026600 * q^66 + 3616484738013649368 * q^67 + 10222742180471202576 * q^68 + 5055175962269366336 * q^69 - 19032968364049376312 * q^70 + 25656771398063139860 * q^72 - 8261076542622345196 * q^73 - 25178485635166968840 * q^74 - 3832367770616596628 * q^75 + 7166640276784437528 * q^76 + 11203664919043126640 * q^78 - 1466375099195149772 * q^79 - 34199363120323087008 * q^80 + 72487941543547369866 * q^81 + 109388057821227568020 * q^82 + 66995861378515080000 * q^83 - 101822670200558802344 * q^84 + 45095997587039885056 * q^85 - 18046647987894919080 * q^86 - 82805580719486000580 * q^87 - 54900983804005197168 * q^88 - 76744426739160882000 * q^89 - 46118057538766055572 * q^90 - 108084262109954148816 * q^91 - 63473510534628793824 * q^92 - 3611178090879526232 * q^93 + 406481789558753974104 * q^94 - 365320875017942904040 * q^96 - 98657490905973791788 * q^97 - 172145012611379837118 * q^98 + 50407643545424273152 * q^99

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.21.b	\(\chi_{24}(19, \cdot)\)	24.21.b.a	40	1
24.21.e	\(\chi_{24}(17, \cdot)\)	24.21.e.a	20	1
24.21.g	\(\chi_{24}(7, \cdot)\)	None	0	1
24.21.h	\(\chi_{24}(5, \cdot)\)	24.21.h.a	1	1
		24.21.h.b	1
		24.21.h.c	76

Decomposition of \(S_{21}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{21}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{21}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{21}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)