Space of modular forms of level 4 and weight 21

• Label: 4.21
• Level: 4
• Weight: 21
• Dimension: 9
• Nonzero newspaces: 1
• Newform subspaces: 2
• Sturm bound: 21
• Trace bound: 0

Defining parameters

Level:	\( N \)	=	\( 4 = 2^{2} \)
Weight:	\( k \)	=	\( 21 \)
Nonzero newspaces:			\( 1 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{21}(\Gamma_1(4))\).

	Total	New	Old
Modular forms	11	11	0
Cusp forms	9	9	0
Eisenstein series	2	2	0

Trace form

9 * q - 628 * q^2 - 267504 * q^4 - 738494 * q^5 + 99460608 * q^6 + 1103532992 * q^8 - 6924577767 * q^9 + 1611884376 * q^10 - 41779799040 * q^12 + 147660923874 * q^13 - 200556776448 * q^14 + 70138216704 * q^16 - 1684556709806 * q^17 + 1635822350412 * q^18 + 241483768096 * q^20 + 33281721747456 * q^21 - 31324969489920 * q^22 - 47563142934528 * q^24 - 567413012949 * q^25 - 63229698776360 * q^26 + 385881741772800 * q^28 + 303916348382242 * q^29 - 1063857826698240 * q^30 + 454535173225472 * q^32 + 1131041167426560 * q^33 - 4199565255965160 * q^34 + 16320708718416912 * q^36 - 7415248775263806 * q^37 - 19214136907706880 * q^38 + 42169382228654976 * q^40 - 5755597456531022 * q^41 - 92697489416232960 * q^42 + 157933848933319680 * q^44 + 22280783580364386 * q^45 - 271527229329687552 * q^46 + 485296685862666240 * q^48 - 37006326729654807 * q^49 - 623084159258016924 * q^50 + 813052968459434784 * q^52 + 132739492344115714 * q^53 - 1607547577815069696 * q^54 + 1749313578676543488 * q^56 + 440441203792112640 * q^57 - 1972695284657517096 * q^58 + 2279505537583872000 * q^60 - 1172450092804974942 * q^61 - 1243411198213386240 * q^62 + 1333510659266973696 * q^64 - 828610552028041948 * q^65 - 21993146403409920 * q^66 - 1641594099654542816 * q^68 + 3450619355851659264 * q^69 + 8506721176491632640 * q^70 - 19477455141526114368 * q^72 - 4955973119248806606 * q^73 + 23508341140743382360 * q^74 - 26576303558589158400 * q^76 - 5280312525070141440 * q^77 + 39300720744848010240 * q^78 - 53478714049403538944 * q^80 + 27869130702616624425 * q^81 + 59306974273770046104 * q^82 - 85636060864270565376 * q^84 + 5624508021574984452 * q^85 + 60721004056878217728 * q^86 - 36088003765030440960 * q^88 - 30717207683107545998 * q^89 + 14470051757664399576 * q^90 + 64932970344704317440 * q^92 - 53255995615294218240 * q^93 - 49076400009934399488 * q^94 + 148896006651003076608 * q^96 + 21227709255069480594 * q^97 - 274458557005261496308 * q^98

Decomposition of \(S_{21}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.21.b	\(\chi_{4}(3, \cdot)\)	4.21.b.a	1	1
		4.21.b.b	8