Space of modular forms of level 74 and weight 8

• Label: 74.8
• Level: 74
• Weight: 8
• Dimension: 397
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 2736
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2736\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(74))\).

	Total	New	Old
Modular forms	1233	397	836
Cusp forms	1161	397	764
Eisenstein series	72	0	72

Trace form

397 * q + 16 * q^2 - 24 * q^3 - 128 * q^4 + 420 * q^5 + 192 * q^6 - 2032 * q^7 + 1024 * q^8 + 4086 * q^9 - 3360 * q^10 - 2184 * q^11 - 1536 * q^12 - 2764 * q^13 + 16256 * q^14 + 5040 * q^15 - 8192 * q^16 - 29412 * q^17 - 32688 * q^18 + 79880 * q^19 + 26880 * q^20 - 24384 * q^21 + 17472 * q^22 - 137424 * q^23 + 12288 * q^24 + 68050 * q^25 + 814328 * q^26 - 843264 * q^27 - 516352 * q^28 - 69576 * q^29 + 1374912 * q^30 + 3120668 * q^31 + 65536 * q^32 + 710568 * q^33 - 788256 * q^34 - 3428772 * q^35 - 1838016 * q^36 - 3740858 * q^37 - 1473952 * q^38 + 617748 * q^39 + 1697280 * q^40 + 7617048 * q^41 + 6058176 * q^42 + 5979872 * q^43 - 139776 * q^44 - 6448032 * q^45 - 8097600 * q^46 - 7035180 * q^47 - 1425408 * q^48 + 6606366 * q^49 + 6120424 * q^50 - 352944 * q^51 - 176896 * q^52 + 2988036 * q^53 - 812160 * q^54 + 458640 * q^55 + 1040384 * q^56 + 958560 * q^57 - 1641120 * q^58 - 2217972 * q^59 + 322560 * q^60 - 17429389 * q^61 + 3640832 * q^62 + 2137500 * q^63 - 524288 * q^64 + 23156679 * q^65 + 209664 * q^66 + 10380860 * q^67 - 1882368 * q^68 + 4733424 * q^69 - 3413760 * q^70 - 14633640 * q^71 - 2092032 * q^72 - 29969788 * q^73 + 1284208 * q^74 - 51889380 * q^75 + 5112320 * q^76 - 909480 * q^77 + 265344 * q^78 + 35195816 * q^79 + 1720320 * q^80 + 77421726 * q^81 + 173472 * q^82 + 3472284 * q^83 - 1560576 * q^84 - 9905301 * q^85 - 10091968 * q^86 - 98926884 * q^87 + 1118208 * q^88 - 17705385 * q^89 + 6864480 * q^90 + 113728720 * q^91 + 41554176 * q^92 - 60183444 * q^93 - 84827328 * q^94 - 208276800 * q^95 + 786432 * q^96 - 74564404 * q^97 + 29548560 * q^98 + 124970652 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(74))\)

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
74.8.a	\(\chi_{74}(1, \cdot)\)	74.8.a.a	4	1
		74.8.a.b	4
		74.8.a.c	6
		74.8.a.d	7
74.8.b	\(\chi_{74}(73, \cdot)\)	74.8.b.a	24	1
74.8.c	\(\chi_{74}(47, \cdot)\)	74.8.c.a	22	2
		74.8.c.b	24
74.8.e	\(\chi_{74}(11, \cdot)\)	74.8.e.a	48	2
74.8.f	\(\chi_{74}(7, \cdot)\)	74.8.f.a	60	6
		74.8.f.b	66
74.8.h	\(\chi_{74}(3, \cdot)\)	74.8.h.a	132	6

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(74))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(74)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 1}\)