Space of modular forms of level 92 and weight 5

• Label: 92.5
• Level: 92
• Weight: 5
• Dimension: 592
• Nonzero newspaces: 4
• Newform subspaces: 4
• Sturm bound: 2640
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(2640\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(92))\).

	Total	New	Old
Modular forms	1111	632	479
Cusp forms	1001	592	409
Eisenstein series	110	40	70

Trace form

592 * q - 3 * q^2 - 43 * q^4 + 6 * q^5 - 11 * q^6 + 117 * q^8 - 184 * q^9 - 123 * q^10 - 11 * q^12 + 454 * q^13 - 11 * q^14 + 1463 * q^15 - 523 * q^16 - 1161 * q^17 + 637 * q^18 - 957 * q^19 + 437 * q^20 - 1375 * q^21 - 22 * q^22 + 990 * q^23 - 22 * q^24 + 3542 * q^25 - 1915 * q^26 + 4785 * q^27 - 11 * q^28 + 507 * q^29 - 11 * q^30 - 1881 * q^31 + 2037 * q^32 - 6677 * q^33 - 10261 * q^34 - 6600 * q^35 - 7058 * q^36 - 826 * q^37 + 10384 * q^38 + 11088 * q^39 + 22397 * q^40 + 11862 * q^41 + 24739 * q^42 + 7216 * q^43 + 6688 * q^44 + 2224 * q^45 - 8019 * q^46 - 7920 * q^47 - 22979 * q^48 - 26472 * q^49 - 32318 * q^50 - 17424 * q^51 - 34745 * q^52 - 12378 * q^53 - 21395 * q^54 + 12474 * q^55 + 5434 * q^56 + 18359 * q^57 + 38540 * q^58 + 9372 * q^59 + 34639 * q^60 - 8590 * q^61 - 11 * q^62 - 27775 * q^63 - 8203 * q^64 - 34637 * q^65 + 880 * q^66 - 2926 * q^67 - 10326 * q^68 + 7513 * q^69 - 22 * q^70 + 21945 * q^71 + 11248 * q^72 + 10404 * q^73 + 43652 * q^74 + 17127 * q^75 + 60214 * q^76 - 15631 * q^77 + 18579 * q^78 + 21604 * q^79 - 35314 * q^80 + 64692 * q^81 - 73617 * q^82 - 11253 * q^83 - 128293 * q^84 + 88304 * q^85 - 80861 * q^86 + 41712 * q^87 - 44099 * q^88 + 42462 * q^89 - 46670 * q^90 + 18106 * q^92 - 96140 * q^93 + 53328 * q^94 + 5115 * q^95 + 174504 * q^96 - 5459 * q^97 + 109749 * q^98 - 48477 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(92))\)

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
92.5.c	\(\chi_{92}(47, \cdot)\)	92.5.c.a	44	1
92.5.d	\(\chi_{92}(45, \cdot)\)	92.5.d.a	8	1
92.5.f	\(\chi_{92}(5, \cdot)\)	92.5.f.a	80	10
92.5.g	\(\chi_{92}(3, \cdot)\)	92.5.g.a	460	10

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(92))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(92)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)