Space of modular forms of level 49 and weight 6

• Label: 49.6
• Level: 49
• Weight: 6
• Dimension: 446
• Nonzero newspaces: 4
• Newform subspaces: 17
• Sturm bound: 1176
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 49 = 7^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1176\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(49))\).

	Total	New	Old
Modular forms	520	495	25
Cusp forms	460	446	14
Eisenstein series	60	49	11

Trace form

446 * q - 15 * q^2 + 3 * q^3 - 143 * q^4 + 51 * q^5 + 423 * q^6 + 98 * q^7 + 315 * q^8 - 1803 * q^9 - 3105 * q^10 - 429 * q^11 + 4599 * q^12 + 4655 * q^13 + 1722 * q^14 - 1863 * q^15 - 7223 * q^16 - 4869 * q^17 - 7611 * q^18 + 5987 * q^19 + 9387 * q^20 + 1113 * q^21 - 399 * q^22 - 7869 * q^23 - 3609 * q^24 + 10177 * q^25 - 4557 * q^26 - 6885 * q^27 + 518 * q^28 + 7941 * q^29 + 39711 * q^30 + 22403 * q^31 + 1485 * q^32 - 40353 * q^33 - 76017 * q^34 - 29379 * q^35 - 80505 * q^36 - 41721 * q^37 + 66867 * q^38 + 108654 * q^39 + 235083 * q^40 + 115689 * q^41 + 143997 * q^42 + 66503 * q^43 + 31875 * q^44 - 106716 * q^45 - 224025 * q^46 - 174879 * q^47 - 442278 * q^48 - 201544 * q^49 - 241350 * q^50 - 173817 * q^51 - 118125 * q^52 + 5325 * q^53 + 426207 * q^54 + 483270 * q^55 + 484092 * q^56 + 217419 * q^57 + 215031 * q^58 + 100089 * q^59 + 117075 * q^60 - 73176 * q^61 - 229821 * q^62 - 362838 * q^63 - 258473 * q^64 - 100149 * q^65 - 250401 * q^66 + 131843 * q^67 + 275079 * q^68 + 237219 * q^69 + 130473 * q^70 - 68919 * q^71 - 116307 * q^72 - 272101 * q^73 - 389589 * q^74 - 151917 * q^75 - 116473 * q^76 - 73395 * q^77 - 64743 * q^78 - 148093 * q^79 - 857700 * q^80 - 515355 * q^81 - 317016 * q^82 + 517167 * q^83 + 1595286 * q^84 + 830997 * q^85 + 2040834 * q^86 + 1815267 * q^87 + 1842588 * q^88 + 305223 * q^89 + 431178 * q^90 - 104279 * q^91 - 830574 * q^92 - 1071189 * q^93 - 1142040 * q^94 - 1783173 * q^95 - 3666558 * q^96 - 1551466 * q^97 - 2833740 * q^98 - 1126668 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.6.a	\(\chi_{49}(1, \cdot)\)	49.6.a.a	1	1
		49.6.a.b	1
		49.6.a.c	2
		49.6.a.d	2
		49.6.a.e	2
		49.6.a.f	2
		49.6.a.g	4
49.6.c	\(\chi_{49}(18, \cdot)\)	49.6.c.a	2	2
		49.6.c.b	2
		49.6.c.c	2
		49.6.c.d	4
		49.6.c.e	4
		49.6.c.f	4
		49.6.c.g	4
		49.6.c.h	8
49.6.e	\(\chi_{49}(8, \cdot)\)	49.6.e.a	138	6
49.6.g	\(\chi_{49}(2, \cdot)\)	49.6.g.a	264	12

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)