Space of modular forms of level 49 and weight 3

• Label: 49.3
• Level: 49
• Weight: 3
• Dimension: 164
• Nonzero newspaces: 4
• Newform subspaces: 5
• Sturm bound: 588
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 49 = 7^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 5 \)
Sturm bound:			\(588\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(49))\).

	Total	New	Old
Modular forms	226	212	14
Cusp forms	166	164	2
Eisenstein series	60	48	12

Trace form

164 * q - 15 * q^2 - 21 * q^3 - 31 * q^4 - 21 * q^5 - 21 * q^6 - 14 * q^7 - 33 * q^8 - 39 * q^9 - 21 * q^10 - 9 * q^11 - 21 * q^12 - 21 * q^13 - 42 * q^14 - 39 * q^15 + q^16 - 21 * q^17 + 33 * q^18 - 21 * q^19 - 21 * q^20 - 21 * q^21 - 75 * q^22 - 57 * q^23 - 21 * q^24 - 71 * q^25 - 21 * q^26 - 21 * q^27 + 14 * q^28 + 69 * q^29 - 21 * q^30 - 21 * q^31 - 111 * q^32 - 21 * q^33 - 21 * q^34 - 21 * q^35 + 195 * q^36 + 363 * q^37 + 399 * q^38 + 420 * q^39 + 987 * q^40 + 273 * q^41 + 483 * q^42 + 55 * q^43 + 543 * q^44 + 294 * q^45 + 339 * q^46 + 21 * q^47 - 154 * q^49 - 78 * q^50 - 273 * q^51 - 637 * q^52 - 219 * q^53 - 777 * q^54 - 756 * q^55 - 1050 * q^56 - 417 * q^57 - 1185 * q^58 - 483 * q^59 - 1533 * q^60 - 658 * q^61 - 609 * q^62 - 378 * q^63 - 433 * q^64 - 21 * q^65 - 21 * q^66 + 215 * q^67 - 21 * q^68 - 21 * q^69 - 21 * q^70 - 267 * q^71 + 33 * q^72 - 21 * q^73 - 249 * q^74 - 21 * q^75 - 21 * q^76 - 63 * q^77 + 609 * q^78 + 167 * q^79 + 1050 * q^80 + 1161 * q^81 + 1554 * q^82 + 1155 * q^83 + 2982 * q^84 + 969 * q^85 + 1944 * q^86 + 1659 * q^87 + 2022 * q^88 + 651 * q^89 + 2772 * q^90 + 483 * q^91 + 516 * q^92 + 987 * q^93 + 546 * q^94 + 315 * q^95 + 420 * q^96 - 168 * q^98 - 288 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.3.b	\(\chi_{49}(48, \cdot)\)	49.3.b.a	4	1
49.3.d	\(\chi_{49}(19, \cdot)\)	49.3.d.a	2	2
		49.3.d.b	8
49.3.f	\(\chi_{49}(6, \cdot)\)	49.3.f.a	54	6
49.3.h	\(\chi_{49}(3, \cdot)\)	49.3.h.a	96	12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 1}\)