Space of modular forms of level 49 and weight 2

• Label: 49.2
• Level: 49
• Weight: 2
• Dimension: 69
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 392
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 49 = 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(392\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(49))\).

	Total	New	Old
Modular forms	128	118	10
Cusp forms	69	69	0
Eisenstein series	59	49	10

Trace form

69 * q - 18 * q^2 - 17 * q^3 - 14 * q^4 - 15 * q^5 - 9 * q^6 - 14 * q^7 - 24 * q^8 - 8 * q^9 - 3 * q^10 - 9 * q^11 + 7 * q^12 - 7 * q^13 - 15 * q^15 + 10 * q^16 - 3 * q^17 + 18 * q^18 - q^19 + 21 * q^20 + 7 * q^21 - 3 * q^22 + 3 * q^23 + 39 * q^24 + 10 * q^25 + 21 * q^26 + 19 * q^27 + 28 * q^28 - 9 * q^29 + 51 * q^30 + 11 * q^31 + 42 * q^32 + 27 * q^33 + 33 * q^34 + 21 * q^35 - 2 * q^36 - 11 * q^37 - 3 * q^38 - 14 * q^39 - 57 * q^40 - 21 * q^41 - 21 * q^42 - 37 * q^43 - 63 * q^44 - 48 * q^45 - 75 * q^46 - 15 * q^47 - 72 * q^48 - 56 * q^49 - 51 * q^50 - 33 * q^51 - 77 * q^52 - 9 * q^53 - 27 * q^54 - 54 * q^55 - 42 * q^56 - q^57 - 15 * q^58 - 3 * q^59 + 21 * q^60 - 8 * q^61 + 33 * q^62 + 42 * q^63 + 16 * q^64 + 63 * q^65 + 123 * q^66 + 47 * q^67 + 105 * q^68 + 75 * q^69 + 105 * q^70 + 33 * q^71 + 174 * q^72 + 53 * q^73 + 93 * q^74 + 103 * q^75 + 119 * q^76 + 63 * q^77 + 21 * q^78 + 59 * q^79 + 102 * q^80 + 16 * q^81 - 21 * q^83 - 56 * q^84 - 15 * q^85 - 36 * q^86 - 69 * q^87 - 72 * q^88 - 15 * q^89 - 186 * q^90 - 7 * q^91 - 18 * q^92 - 145 * q^93 - 66 * q^94 - 69 * q^95 - 168 * q^96 - 28 * q^97 - 168 * q^98 - 72 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.2.a	\(\chi_{49}(1, \cdot)\)	49.2.a.a	1	1
49.2.c	\(\chi_{49}(18, \cdot)\)	49.2.c.a	2	2
49.2.e	\(\chi_{49}(8, \cdot)\)	49.2.e.a	6	6
		49.2.e.b	12
49.2.g	\(\chi_{49}(2, \cdot)\)	49.2.g.a	48	12