Space of modular forms of level 16 and weight 9

• Label: 16.9
• Level: 16
• Weight: 9
• Dimension: 34
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 144
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 16 = 2^{4} \)
Weight:	\( k \)	=	\( 9 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(144\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(16))\).

	Total	New	Old
Modular forms	71	38	33
Cusp forms	57	34	23
Eisenstein series	14	4	10

Trace form

34 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 506 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 14460 * q^9 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 17146 * q^13 - 58900 * q^14 + 245336 * q^16 - 16636 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 + 621244 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 909172 * q^25 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 2860486 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 6084868 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 9044934 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 8799480 * q^41 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 17951754 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 3067998 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 27396166 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 26616576 * q^57 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 55299706 * q^61 - 64043472 * q^62 + 50827456 * q^64 + 23168588 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 - 33968324 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 + 38504968 * q^73 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 - 18785860 * q^77 + 5059788 * q^78 - 12904856 * q^80 + 116973410 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 189400628 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 + 139985928 * q^89 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 - 224712320 * q^93 - 239278032 * q^94 + 378359728 * q^96 + 148649220 * q^97 + 630040554 * q^98 + 184838270 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.9.c	\(\chi_{16}(15, \cdot)\)	16.9.c.a	2	1
		16.9.c.b	2
16.9.d	\(\chi_{16}(7, \cdot)\)	None	0	1
16.9.f	\(\chi_{16}(3, \cdot)\)	16.9.f.a	30	2

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(16))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(16)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)