Space of modular forms of level 49 and weight 7

• Label: 49.7
• Level: 49
• Weight: 7
• Dimension: 540
• Nonzero newspaces: 4
• Newform subspaces: 10
• Sturm bound: 1372
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 49 = 7^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1372\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(49))\).

	Total	New	Old
Modular forms	618	588	30
Cusp forms	558	540	18
Eisenstein series	60	48	12

Trace form

540 * q - 15 * q^2 - 15 * q^3 - 15 * q^4 - 351 * q^5 - 21 * q^6 + 462 * q^7 + 1383 * q^8 + 3681 * q^9 - 5181 * q^10 - 8247 * q^11 - 11949 * q^12 - 21 * q^13 + 11130 * q^14 + 33621 * q^15 + 20025 * q^16 - 16479 * q^17 - 68439 * q^18 - 59991 * q^19 - 21 * q^20 + 37506 * q^21 + 119781 * q^22 + 9729 * q^23 - 57765 * q^24 - 125511 * q^25 - 67557 * q^26 - 21 * q^27 + 23814 * q^28 + 50997 * q^29 + 86379 * q^30 + 78777 * q^31 + 112089 * q^32 + 73401 * q^33 - 21 * q^34 - 74886 * q^35 + 44103 * q^36 + 8889 * q^37 - 486501 * q^38 - 300069 * q^39 - 1080213 * q^40 - 174069 * q^41 + 66003 * q^42 - 50139 * q^43 + 1815567 * q^44 + 2169879 * q^45 + 2348247 * q^46 + 1086105 * q^47 - 917238 * q^49 - 2132478 * q^50 - 2730855 * q^51 - 3362373 * q^52 - 913095 * q^53 - 1625637 * q^54 - 511581 * q^55 + 771834 * q^56 + 1662549 * q^57 + 3372759 * q^58 + 2476641 * q^59 + 4988067 * q^60 + 680721 * q^61 - 787941 * q^62 - 2231586 * q^63 - 2171337 * q^64 - 420861 * q^65 - 2051085 * q^66 - 3275679 * q^67 - 1599213 * q^68 - 21 * q^69 + 1863099 * q^70 + 3777909 * q^71 + 3019497 * q^72 + 843177 * q^73 - 347649 * q^74 - 1652121 * q^75 - 21 * q^76 - 709506 * q^77 + 178521 * q^78 - 866559 * q^79 + 5660010 * q^80 - 676557 * q^81 - 9899778 * q^82 - 7043085 * q^83 - 19204038 * q^84 - 2169531 * q^85 - 2573748 * q^86 + 303231 * q^87 + 3646374 * q^88 + 9392025 * q^89 + 25307352 * q^90 + 7257579 * q^91 + 10776660 * q^92 + 14349033 * q^93 + 12710046 * q^94 + 6111825 * q^95 + 7789488 * q^96 - 11781336 * q^98 - 11388816 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.7.b	\(\chi_{49}(48, \cdot)\)	49.7.b.a	2	1
		49.7.b.b	4
		49.7.b.c	12
49.7.d	\(\chi_{49}(19, \cdot)\)	49.7.d.a	2	2
		49.7.d.b	2
		49.7.d.c	4
		49.7.d.d	4
		49.7.d.e	24
49.7.f	\(\chi_{49}(6, \cdot)\)	49.7.f.a	162	6
49.7.h	\(\chi_{49}(3, \cdot)\)	49.7.h.a	324	12

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

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