Space of modular forms of level 8 and weight 14

• Label: 8.14
• Level: 8
• Weight: 14
• Dimension: 15
• Nonzero newspaces: 2
• Newform subspaces: 4
• Sturm bound: 56
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 8 = 2^{3} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(8))\).

	Total	New	Old
Modular forms	29	17	12
Cusp forms	23	15	8
Eisenstein series	6	2	4

Trace form

15 * q - 2 * q^2 + 860 * q^3 - 8556 * q^4 + 14146 * q^5 + 58444 * q^6 + 206232 * q^7 + 1076872 * q^8 - 3319093 * q^9 - 7752648 * q^10 + 9989716 * q^11 - 8536664 * q^12 - 3843462 * q^13 + 21101872 * q^14 + 42509064 * q^15 - 62847216 * q^16 - 227240498 * q^17 + 262778834 * q^18 + 206597196 * q^19 + 381237904 * q^20 - 1370300832 * q^21 + 196775484 * q^22 + 1490018760 * q^23 + 1739438480 * q^24 - 4205723223 * q^25 - 685452248 * q^26 + 5792047640 * q^27 - 978617568 * q^28 - 3556537878 * q^29 + 539961392 * q^30 - 7367666592 * q^31 - 8956909792 * q^32 + 14055767168 * q^33 + 8857451100 * q^34 - 15413225904 * q^35 + 18075363660 * q^36 + 6628831266 * q^37 - 23710846420 * q^38 + 20630243496 * q^39 - 6505554528 * q^40 + 47965956118 * q^41 - 3443304224 * q^42 - 46788121548 * q^43 - 28647791928 * q^44 + 107010747322 * q^45 - 51061300848 * q^46 - 201450140016 * q^47 - 161587694304 * q^48 + 101164221495 * q^49 + 246819442102 * q^50 + 177530164600 * q^51 + 441779820720 * q^52 - 125287225454 * q^53 - 639572716168 * q^54 + 217008668376 * q^55 - 699100837568 * q^56 - 1007795333472 * q^57 + 992195908104 * q^58 + 793560430372 * q^59 + 1614284565792 * q^60 - 698520953142 * q^61 - 1019628353344 * q^62 - 426693206408 * q^63 - 1464077986752 * q^64 - 357709159492 * q^65 + 2946347707608 * q^66 + 1645513736988 * q^67 + 2850998874984 * q^68 + 1015234563872 * q^69 - 5505591528768 * q^70 - 4320352976296 * q^71 - 8538615449032 * q^72 + 3510289845750 * q^73 + 9399657781240 * q^74 + 844579119460 * q^75 + 10892359157736 * q^76 + 1067266262304 * q^77 - 16235130104944 * q^78 - 1836704085264 * q^79 - 16787669526720 * q^80 + 3452732525415 * q^81 + 14910525285612 * q^82 + 3890337600524 * q^83 + 26784826987072 * q^84 + 1613607983652 * q^85 - 24718490913284 * q^86 - 14659545283608 * q^87 - 26046521626416 * q^88 - 745298334170 * q^89 + 43218339424520 * q^90 + 19047242532624 * q^91 + 34108342295904 * q^92 - 6946080702080 * q^93 - 37727942061792 * q^94 - 25493775576920 * q^95 - 62733552180160 * q^96 - 15392053442370 * q^97 + 61714328751438 * q^98 + 42866396476420 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.14.a	\(\chi_{8}(1, \cdot)\)	8.14.a.a	1	1
		8.14.a.b	2
8.14.b	\(\chi_{8}(5, \cdot)\)	8.14.b.a	2	1
		8.14.b.b	10

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

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