Space of modular forms of level 46, weight 8, and trivial character

• Label: 46.8.a
• Level: $46$
• Weight: $8$
• Character orbit: 46.a
• Rep. character: $\chi_{46}(1,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	46.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(46))\).

	Total	New	Old
Modular forms	44	12	32
Cusp forms	40	12	28
Eisenstein series	4	0	4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)	\(23\)	Fricke	Dim
\(+\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(2\)
\(-\)	\(+\)	\(-\)	\(3\)
\(-\)	\(-\)	\(+\)	\(4\)
Plus space		\(+\)	\(7\)
Minus space		\(-\)	\(5\)

Trace form

12 * q + 16 * q^2 + 28 * q^3 + 768 * q^4 - 110 * q^5 + 1120 * q^6 - 1244 * q^7 + 1024 * q^8 + 8468 * q^9 - 5360 * q^10 - 12178 * q^11 + 1792 * q^12 - 3168 * q^13 - 3616 * q^14 + 53464 * q^15 + 49152 * q^16 - 83900 * q^17 + 22480 * q^18 + 95778 * q^19 - 7040 * q^20 - 92312 * q^21 - 9648 * q^22 + 71680 * q^24 + 227368 * q^25 + 34272 * q^26 + 158680 * q^27 - 79616 * q^28 + 494876 * q^29 - 208320 * q^30 - 188624 * q^31 + 65536 * q^32 + 105336 * q^33 + 222336 * q^34 + 486944 * q^35 + 541952 * q^36 - 253974 * q^37 - 813264 * q^38 - 970632 * q^39 - 343040 * q^40 - 299388 * q^41 + 171776 * q^42 - 1262602 * q^43 - 779392 * q^44 + 153154 * q^45 + 194672 * q^46 - 572256 * q^47 + 114688 * q^48 + 3241580 * q^49 - 1042992 * q^50 - 2067208 * q^51 - 202752 * q^52 - 881854 * q^53 + 3254464 * q^54 + 1735552 * q^55 - 231424 * q^56 - 6212080 * q^57 - 3102976 * q^58 - 3906240 * q^59 + 3421696 * q^60 + 6632366 * q^61 + 5464576 * q^62 + 2211684 * q^63 + 3145728 * q^64 - 3058076 * q^65 - 8469120 * q^66 - 7988886 * q^67 - 5369600 * q^68 + 1314036 * q^69 - 6746880 * q^70 + 680712 * q^71 + 1438720 * q^72 - 8446764 * q^73 + 1847504 * q^74 + 18952868 * q^75 + 6129792 * q^76 + 14568712 * q^77 + 5054272 * q^78 + 5871108 * q^79 - 450560 * q^80 + 1591196 * q^81 + 5102464 * q^82 + 3549170 * q^83 - 5907968 * q^84 - 10402524 * q^85 - 6403824 * q^86 - 6389800 * q^87 - 617472 * q^88 + 17225208 * q^89 + 11425616 * q^90 - 6570056 * q^91 + 28532136 * q^93 - 10091136 * q^94 - 7329632 * q^95 + 4587520 * q^96 - 38850324 * q^97 + 893712 * q^98 - 4181946 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(46))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	23
46.8.a.a	$46$	$8$	46.a	1.a	$1$	$2$	$2$	$14.370$	\(\Q(\sqrt{85}) \)	None	✓	✓	✓	✓	46.8.a.a	$1$	$1$	\(-16\)	\(-28\)	\(-110\)	\(74\)		$+$	$-$	$-$	$2$	$\mathrm{SU}(2)$	\(q-8q^{2}+(-14-7\beta )q^{3}+2^{6}q^{4}+(-55+\cdots)q^{5}+\cdots\)
46.8.a.b	$46$	$8$	46.a	1.a	$1$	$3$	$3$	$14.370$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	✓	✓	✓	46.8.a.b	$1$	$0$	\(-24\)	\(-28\)	\(390\)	\(-470\)		$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	\(q-8q^{2}+(-9-\beta _{2})q^{3}+2^{6}q^{4}+(131+\cdots)q^{5}+\cdots\)
46.8.a.c	$46$	$8$	46.a	1.a	$1$	$3$	$3$	$14.370$	3.3.285765.1	None	✓	✓	✓	✓	46.8.a.c	$1$	$1$	\(24\)	\(-12\)	\(-570\)	\(-1382\)		$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	\(q+8q^{2}+(-5+2\beta _{1}-\beta _{2})q^{3}+2^{6}q^{4}+\cdots\)
46.8.a.d	$46$	$8$	46.a	1.a	$1$	$4$	$4$	$14.370$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	✓	✓	✓	46.8.a.d	$1$	$0$	\(32\)	\(96\)	\(180\)	\(534\)		$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	\(q+8q^{2}+(24-\beta _{1})q^{3}+2^{6}q^{4}+(45+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(46))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(46)) \simeq \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)