Space of modular forms of level 40 and weight 12

• Label: 40.12
• Level: 40
• Weight: 12
• Dimension: 263
• Nonzero newspaces: 5
• Newform subspaces: 9
• Sturm bound: 1152
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1152\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(40))\).

	Total	New	Old
Modular forms	552	275	277
Cusp forms	504	263	241
Eisenstein series	48	12	36

Trace form

263 * q - 48 * q^2 - 44 * q^3 - 876 * q^4 + 2091 * q^5 + 48608 * q^6 - 35464 * q^7 + 416940 * q^8 + 511323 * q^9 - 29868 * q^10 + 217596 * q^11 + 1661016 * q^12 - 2286454 * q^13 - 2847936 * q^14 - 7698676 * q^15 + 907624 * q^16 - 26992986 * q^17 - 18942100 * q^18 + 28614804 * q^19 - 29676016 * q^20 - 25451608 * q^21 + 146868320 * q^22 + 108462000 * q^23 - 260905864 * q^24 - 366899753 * q^25 + 321764728 * q^26 + 33845704 * q^27 + 100899384 * q^28 + 444562098 * q^29 - 325057168 * q^30 - 1033322528 * q^31 - 266511768 * q^32 + 400508184 * q^33 + 633409156 * q^34 + 1626705176 * q^35 - 1006391360 * q^36 + 182616018 * q^37 + 645286096 * q^38 - 5377751496 * q^39 + 1128683572 * q^40 + 1123005294 * q^41 + 2878830608 * q^42 + 8901161756 * q^43 + 6050461888 * q^44 - 6347148113 * q^45 - 5001250352 * q^46 - 7044434408 * q^47 - 8642278632 * q^48 + 2098788559 * q^49 - 4948899508 * q^50 + 10748475608 * q^51 + 23712981140 * q^52 - 2251348718 * q^53 - 21759527992 * q^54 - 481422444 * q^55 - 18367650512 * q^56 + 13935801408 * q^57 + 21976819228 * q^58 - 6851078836 * q^59 + 8224963912 * q^60 + 1789732762 * q^61 - 52876800272 * q^62 - 11451199416 * q^63 - 33925860192 * q^64 - 10661402582 * q^65 + 104183372080 * q^66 - 63719296188 * q^67 + 66932451844 * q^68 + 32885696312 * q^69 - 25128293688 * q^70 + 56860327576 * q^71 - 111663658300 * q^72 + 3644583446 * q^73 + 25597176348 * q^74 - 159534313860 * q^75 + 225491014896 * q^76 - 46171111648 * q^77 - 108962438888 * q^78 + 27146206032 * q^79 - 20921065720 * q^80 + 79064064807 * q^81 + 93155657244 * q^82 - 16677284596 * q^83 + 173130738336 * q^84 + 45915418102 * q^85 - 130505793680 * q^86 + 98807843776 * q^87 - 406873709376 * q^88 - 112942802186 * q^89 + 339398038980 * q^90 + 154939171536 * q^91 + 336441145392 * q^92 + 189017930800 * q^93 - 131890588600 * q^94 - 292255456740 * q^95 + 145011747952 * q^96 - 194631930594 * q^97 - 428356688728 * q^98 - 181067793324 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(40))\)

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
40.12.a	\(\chi_{40}(1, \cdot)\)	40.12.a.a	1	1
		40.12.a.b	2
		40.12.a.c	2
		40.12.a.d	3
		40.12.a.e	3
40.12.c	\(\chi_{40}(9, \cdot)\)	40.12.c.a	16	1
40.12.d	\(\chi_{40}(21, \cdot)\)	40.12.d.a	44	1
40.12.f	\(\chi_{40}(29, \cdot)\)	40.12.f.a	64	1
40.12.j	\(\chi_{40}(7, \cdot)\)	None	0	2
40.12.k	\(\chi_{40}(3, \cdot)\)	40.12.k.a	128	2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(40))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(40)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)