Space of modular forms of level 92 and weight 4

• Label: 92.4
• Level: 92
• Weight: 4
• Dimension: 440
• Nonzero newspaces: 4
• Newform subspaces: 7
• Sturm bound: 2112
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(2112\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(92))\).

	Total	New	Old
Modular forms	847	484	363
Cusp forms	737	440	297
Eisenstein series	110	44	66

Trace form

440 * q - 11 * q^2 - 11 * q^4 - 22 * q^5 - 11 * q^6 - 11 * q^8 - 22 * q^9 - 11 * q^10 - 11 * q^12 - 22 * q^13 - 11 * q^14 - 374 * q^15 - 11 * q^16 - 110 * q^17 - 11 * q^18 + 110 * q^19 - 11 * q^20 + 638 * q^21 + 484 * q^23 - 22 * q^24 + 330 * q^25 - 11 * q^26 + 66 * q^27 - 11 * q^28 - 242 * q^29 - 11 * q^30 - 550 * q^31 - 11 * q^32 - 990 * q^33 + 1903 * q^34 + 1430 * q^35 + 2464 * q^36 + 1166 * q^37 + 594 * q^38 - 132 * q^39 - 1331 * q^40 - 572 * q^41 - 3641 * q^42 - 1716 * q^43 - 3322 * q^44 - 2970 * q^45 - 3971 * q^46 - 1892 * q^47 - 3443 * q^48 - 2200 * q^49 - 1936 * q^50 - 660 * q^51 - 341 * q^52 + 220 * q^53 + 2365 * q^54 - 528 * q^55 + 3564 * q^56 + 1694 * q^57 + 6094 * q^58 + 2046 * q^59 + 3619 * q^60 + 506 * q^61 - 11 * q^62 + 2090 * q^63 - 11 * q^64 + 4290 * q^65 - 308 * q^66 + 1452 * q^67 + 3718 * q^69 - 22 * q^70 + 3410 * q^71 + 286 * q^72 + 1034 * q^73 - 2376 * q^74 + 5984 * q^75 - 8206 * q^76 + 10230 * q^77 - 10021 * q^78 - 418 * q^79 - 4070 * q^80 - 1386 * q^81 + 55 * q^82 - 5104 * q^83 + 5379 * q^84 - 12056 * q^85 + 6699 * q^86 - 4686 * q^87 + 6941 * q^88 - 5632 * q^89 + 18678 * q^90 - 4004 * q^91 + 8998 * q^92 - 23540 * q^93 + 8492 * q^94 - 6402 * q^95 + 14828 * q^96 - 10384 * q^97 + 4301 * q^98 - 9240 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)

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
92.4.a	\(\chi_{92}(1, \cdot)\)	92.4.a.a	3	1
		92.4.a.b	3
92.4.b	\(\chi_{92}(91, \cdot)\)	92.4.b.a	2	1
		92.4.b.b	4
		92.4.b.c	28
92.4.e	\(\chi_{92}(9, \cdot)\)	92.4.e.a	60	10
92.4.h	\(\chi_{92}(7, \cdot)\)	92.4.h.a	340	10

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(92))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(92)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)