Space of modular forms of level 106 and weight 2

• Label: 106.2
• Level: 106
• Weight: 2
• Dimension: 116
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 1404
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 106 = 2 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(1404\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(106))\).

	Total	New	Old
Modular forms	403	116	287
Cusp forms	300	116	184
Eisenstein series	103	0	103

Trace form

116 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 - 6 * q^10 - 12 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 - 24 * q^15 - q^16 - 18 * q^17 - 13 * q^18 - 20 * q^19 - 6 * q^20 - 32 * q^21 - 12 * q^22 - 24 * q^23 - 4 * q^24 - 31 * q^25 - 14 * q^26 - 40 * q^27 - 8 * q^28 - 30 * q^29 - 24 * q^30 - 32 * q^31 - q^32 - 48 * q^33 - 18 * q^34 - 48 * q^35 - 13 * q^36 - 38 * q^37 - 20 * q^38 - 56 * q^39 + 7 * q^40 + 10 * q^41 + 72 * q^42 + 60 * q^43 - 12 * q^44 + 182 * q^45 + 28 * q^46 + 4 * q^47 + 48 * q^48 + 47 * q^49 + 86 * q^50 + 136 * q^51 + 38 * q^52 + 103 * q^53 + 116 * q^54 + 84 * q^55 + 44 * q^56 + 128 * q^57 + 87 * q^58 + 44 * q^59 + 28 * q^60 - 10 * q^61 + 20 * q^62 + 156 * q^63 - q^64 + 20 * q^65 + 56 * q^66 - 16 * q^67 - 5 * q^68 - 96 * q^69 - 48 * q^70 - 72 * q^71 - 13 * q^72 - 74 * q^73 - 38 * q^74 - 124 * q^75 - 20 * q^76 - 96 * q^77 - 56 * q^78 - 80 * q^79 - 6 * q^80 - 121 * q^81 - 42 * q^82 - 84 * q^83 - 32 * q^84 - 108 * q^85 - 44 * q^86 - 68 * q^87 - 12 * q^88 - 25 * q^89 - 78 * q^90 - 8 * q^91 - 24 * q^92 - 24 * q^93 - 48 * q^94 - 16 * q^95 - 4 * q^96 + 123 * q^97 - 57 * q^98 + 104 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)

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
106.2.a	\(\chi_{106}(1, \cdot)\)	106.2.a.a	1	1
		106.2.a.b	1
		106.2.a.c	1
		106.2.a.d	1
106.2.b	\(\chi_{106}(105, \cdot)\)	106.2.b.a	2	1
		106.2.b.b	2
106.2.d	\(\chi_{106}(13, \cdot)\)	106.2.d.a	24	12
		106.2.d.b	36
106.2.e	\(\chi_{106}(7, \cdot)\)	106.2.e.a	48	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(106))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(106)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)