Space of modular forms of level 16 and weight 2

• Label: 16.2
• Level: 16
• Weight: 2
• Dimension: 2
• Nonzero newspaces: 1
• Newform subspaces: 1
• Sturm bound: 32
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 16 = 2^{4} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(16))\).

	Total	New	Old
Modular forms	15	7	8
Cusp forms	2	2	0
Eisenstein series	13	5	8

Trace form

2 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 + 4 * q^6 + 4 * q^8 + 2 * q^11 - 4 * q^12 - 2 * q^13 - 4 * q^14 + 4 * q^15 - 8 * q^16 - 4 * q^17 + 2 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^26 - 8 * q^27 + 8 * q^28 + 6 * q^29 - 4 * q^30 - 16 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 - 4 * q^36 + 6 * q^37 - 12 * q^38 - 8 * q^40 + 10 * q^43 - 4 * q^44 + 2 * q^45 + 12 * q^46 + 16 * q^47 + 8 * q^48 + 6 * q^49 - 6 * q^50 + 4 * q^51 - 4 * q^52 - 10 * q^53 - 8 * q^56 - 12 * q^58 - 6 * q^59 - 18 * q^61 + 16 * q^62 + 4 * q^63 + 4 * q^65 + 4 * q^66 - 10 * q^67 - 12 * q^69 + 8 * q^70 + 4 * q^72 + 6 * q^75 + 12 * q^76 + 4 * q^77 - 4 * q^78 + 8 * q^80 + 10 * q^81 - 2 * q^83 - 8 * q^84 + 4 * q^85 + 8 * q^88 - 4 * q^90 + 4 * q^91 - 24 * q^92 + 16 * q^93 - 16 * q^94 - 12 * q^95 - 16 * q^96 - 4 * q^97 - 6 * q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)

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
16.2.a	\(\chi_{16}(1, \cdot)\)	None	0	1
16.2.b	\(\chi_{16}(9, \cdot)\)	None	0	1
16.2.e	\(\chi_{16}(5, \cdot)\)	16.2.e.a	2	2