Space of modular forms of level 49 and weight 20

• Label: 49.20
• Level: 49
• Weight: 20
• Dimension: 1763
• Nonzero newspaces: 4
• Sturm bound: 3920
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 49 = 7^{2} \)
Weight:	\( k \)	=	\( 20 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(3920\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(49))\).

	Total	New	Old
Modular forms	1892	1812	80
Cusp forms	1832	1763	69
Eisenstein series	60	49	11

Trace form

1763 * q + 441 * q^2 + 11271 * q^3 + 1780785 * q^4 + 2608821 * q^5 - 97835049 * q^6 + 146493634 * q^7 - 1516784181 * q^8 + 2824959426 * q^9 + 5355698559 * q^10 - 7809578721 * q^11 + 87411721383 * q^12 - 252484332555 * q^13 + 127084457010 * q^14 - 791867835711 * q^15 + 434869728585 * q^16 + 210085705593 * q^17 - 4525363472163 * q^18 + 8879770852503 * q^19 - 11790488859765 * q^20 - 4751926305105 * q^21 + 11417260486881 * q^22 - 4195279619685 * q^23 - 96735279006729 * q^24 + 188228944016520 * q^25 - 45918514160253 * q^26 - 267220783782621 * q^27 + 124858417477990 * q^28 + 200359092792843 * q^29 - 407570067282129 * q^30 - 387816560568093 * q^31 + 1986575995290717 * q^32 + 1892024293630035 * q^33 - 6518262416311041 * q^34 + 1268243427950457 * q^35 + 1238834231714007 * q^36 - 12730617341200591 * q^37 + 4176652126027851 * q^38 - 4551829213192338 * q^39 + 38195013490508859 * q^40 - 19078611142105137 * q^41 - 40582559199342531 * q^42 + 32973229064812755 * q^43 + 61773826556661411 * q^44 - 40756471041434412 * q^45 - 118346052322578705 * q^46 + 398368433257233 * q^47 + 306784774448999514 * q^48 + 43578226571218612 * q^49 - 355276483294449726 * q^50 - 69534668080582281 * q^51 + 434264677775210387 * q^52 - 19832239628668173 * q^53 - 72074638206796713 * q^54 - 417671412731928330 * q^55 - 248323514944728132 * q^56 + 186432147608017695 * q^57 + 914235076816353495 * q^58 - 334544863639962723 * q^59 - 1422644960562657405 * q^60 + 629496607546304132 * q^61 + 377517970315309659 * q^62 - 125838066898938198 * q^63 - 1959892659209912649 * q^64 - 224205923595003273 * q^65 + 139017281405002575 * q^66 + 608563737206976327 * q^67 + 851518365031171047 * q^68 - 4708713344492364645 * q^69 + 999052479547466337 * q^70 + 2043369566700941505 * q^71 - 546657382961910675 * q^72 - 1115622695399842671 * q^73 + 4013970708865001883 * q^74 + 2073483008738185719 * q^75 - 8411750964224351289 * q^76 - 2158589629318536477 * q^77 + 9960427954886848761 * q^78 - 3270220750861696653 * q^79 + 13672385702694387516 * q^80 - 4286121438344391654 * q^81 + 29012929246435666224 * q^82 - 21026153606441922309 * q^83 - 56953279824133108122 * q^84 + 11271972371151922065 * q^85 + 66105297541472363034 * q^86 + 3598456083487889115 * q^87 - 88396884925552181316 * q^88 - 42701552257350606699 * q^89 + 74765771882916069570 * q^90 + 34829620676432172353 * q^91 + 5038061315257885890 * q^92 - 23879941638859544913 * q^93 - 42335150399689346352 * q^94 - 101777642954245918077 * q^95 + 85928212258256961474 * q^96 + 70810887907919399184 * q^97 + 115086911675992203276 * q^98 - 113830992298373102328 * q^99

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(49))\)

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
49.20.a	\(\chi_{49}(1, \cdot)\)	49.20.a.a	1	1
		49.20.a.b	1
		49.20.a.c	4
		49.20.a.d	5
		49.20.a.e	8
		49.20.a.f	12
		49.20.a.g	12
		49.20.a.h	20
49.20.c	\(\chi_{49}(18, \cdot)\)	n/a	122	2
49.20.e	\(\chi_{49}(8, \cdot)\)	n/a	522	6
49.20.g	\(\chi_{49}(2, \cdot)\)	n/a	1056	12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)