Space of modular forms of level 16 and weight 14

• Label: 16.14
• Level: 16
• Weight: 14
• Dimension: 56
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 224
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 16 = 2^{4} \)
Weight:	\( k \)	=	\( 14 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(224\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(16))\).

	Total	New	Old
Modular forms	111	61	50
Cusp forms	97	56	41
Eisenstein series	14	5	9

Trace form

56 * q - 2 * q^2 - 730 * q^3 + 360 * q^4 + 16898 * q^5 - 255056 * q^6 + 65232 * q^7 - 1076876 * q^8 + 2329966 * q^9 + 1809804 * q^10 - 12400678 * q^11 - 36466556 * q^12 + 8510578 * q^13 - 32192740 * q^14 + 58267764 * q^15 + 49054360 * q^16 - 2730008 * q^17 - 134185218 * q^18 + 687321870 * q^19 - 337515748 * q^20 - 336081308 * q^21 + 747130500 * q^22 + 210016880 * q^23 + 4015997104 * q^24 + 262952922 * q^25 - 7112421624 * q^26 - 4083419128 * q^27 + 10814980184 * q^28 - 2896564486 * q^29 - 7391197164 * q^30 - 11253200848 * q^31 + 161064008 * q^32 + 7736141596 * q^33 + 21518457652 * q^34 + 9879664412 * q^35 - 45856853012 * q^36 + 3678703338 * q^37 + 42250712128 * q^38 + 21412862896 * q^39 + 62168140552 * q^40 - 24031840452 * q^41 - 221492896520 * q^42 - 55432077854 * q^43 + 260848874692 * q^44 + 43054154358 * q^45 - 86330105076 * q^46 + 264471315568 * q^47 - 204935679512 * q^48 - 463336677588 * q^49 + 726765984390 * q^50 - 726061876588 * q^51 - 560232726988 * q^52 + 277957136506 * q^53 + 183832923424 * q^54 + 273717035856 * q^55 + 377498473624 * q^56 - 211899133472 * q^57 + 770591295576 * q^58 + 501824598898 * q^59 - 1652643345408 * q^60 - 97879627326 * q^61 + 1409787089968 * q^62 + 1185688664340 * q^63 + 1414847226240 * q^64 - 209787473060 * q^65 - 4165850751116 * q^66 - 1523656277410 * q^67 + 1936048158032 * q^68 + 465968180628 * q^69 - 1514955295360 * q^70 + 3548344800592 * q^71 - 931909002396 * q^72 + 1333995927036 * q^73 + 2967549191692 * q^74 - 8210473363842 * q^75 - 6006275999532 * q^76 - 3754874767516 * q^77 + 33537158300 * q^78 + 16841575183008 * q^79 + 3800056341544 * q^80 - 9667864508880 * q^81 - 1354092283296 * q^82 - 11172077966522 * q^83 + 6692487540136 * q^84 + 3003459133036 * q^85 - 2175364294396 * q^86 + 25789862820912 * q^87 - 2008707597832 * q^88 - 3034933603620 * q^89 + 1744037438232 * q^90 - 26049096512156 * q^91 + 5983522987064 * q^92 + 2836230337616 * q^93 - 10384516980592 * q^94 + 46358111232292 * q^95 - 22107121515856 * q^96 + 6262475466824 * q^97 + 27036562854554 * q^98 - 35014268425898 * q^99

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.14.a	\(\chi_{16}(1, \cdot)\)	16.14.a.a	1	1
		16.14.a.b	1
		16.14.a.c	1
		16.14.a.d	1
		16.14.a.e	2
16.14.b	\(\chi_{16}(9, \cdot)\)	None	0	1
16.14.e	\(\chi_{16}(5, \cdot)\)	16.14.e.a	50	2

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)