Space of modular forms of level 46, weight 4, and trivial character

• Label: 46.4.a
• Level: $46$
• Weight: $4$
• Character orbit: 46.a
• Rep. character: $\chi_{46}(1,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $4$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(46))\).

	Total	New	Old
Modular forms	20	6	14
Cusp forms	16	6	10
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
\(+\)	\(+\)	\(+\)	\(2\)
\(+\)	\(-\)	\(-\)	\(1\)
\(-\)	\(+\)	\(-\)	\(1\)
\(-\)	\(-\)	\(+\)	\(2\)
Plus space		\(+\)	\(4\)
Minus space		\(-\)	\(2\)

Trace form

6 * q - 8 * q^3 + 24 * q^4 - 10 * q^5 - 8 * q^6 + 8 * q^7 + 146 * q^9 - 20 * q^10 - 34 * q^11 - 32 * q^12 - 112 * q^13 + 40 * q^14 + 4 * q^15 + 96 * q^16 + 28 * q^17 - 128 * q^18 + 38 * q^19 - 40 * q^20 - 260 * q^21 - 188 * q^22 - 32 * q^24 + 78 * q^25 + 192 * q^26 - 404 * q^27 + 32 * q^28 - 276 * q^29 + 480 * q^30 - 156 * q^31 + 948 * q^33 - 520 * q^34 + 544 * q^35 + 584 * q^36 + 294 * q^37 - 436 * q^38 - 444 * q^39 - 80 * q^40 + 484 * q^41 - 64 * q^42 - 366 * q^43 - 136 * q^44 - 326 * q^45 + 92 * q^46 + 1364 * q^47 - 128 * q^48 - 1154 * q^49 + 728 * q^50 - 988 * q^51 - 448 * q^52 + 690 * q^53 - 128 * q^54 + 1432 * q^55 + 160 * q^56 - 1312 * q^57 + 296 * q^58 + 1136 * q^59 + 16 * q^60 - 642 * q^61 - 848 * q^62 + 420 * q^63 + 384 * q^64 - 2256 * q^65 - 96 * q^66 + 426 * q^67 + 112 * q^68 + 276 * q^69 + 160 * q^70 - 1308 * q^71 - 512 * q^72 - 980 * q^73 + 220 * q^74 - 4432 * q^75 + 152 * q^76 + 216 * q^77 + 640 * q^78 + 1948 * q^79 - 160 * q^80 + 4454 * q^81 + 1016 * q^82 + 2146 * q^83 - 1040 * q^84 + 1636 * q^85 + 1380 * q^86 - 2596 * q^87 - 752 * q^88 - 1044 * q^89 - 4804 * q^90 - 1956 * q^91 + 3804 * q^93 + 1008 * q^94 + 2648 * q^95 - 128 * q^96 - 428 * q^97 + 832 * q^98 + 2586 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(46))\) 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
46.4.a.a	$46$	$4$	46.a	1.a	$1$	$1$	$1$	$2.714$	\(\Q\)	None	✓	✓	✓	✓	46.4.a.a	$1$	$1$	\(-2\)	\(-1\)	\(-10\)	\(-12\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}-q^{3}+4q^{4}-10q^{5}+2q^{6}+\cdots\)
46.4.a.b	$46$	$4$	46.a	1.a	$1$	$1$	$1$	$2.714$	\(\Q\)	None	✓	✓	✓	✓	46.4.a.b	$1$	$1$	\(2\)	\(-9\)	\(-20\)	\(2\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}-9q^{3}+4q^{4}-20q^{5}-18q^{6}+\cdots\)
46.4.a.c	$46$	$4$	46.a	1.a	$1$	$2$	$2$	$2.714$	\(\Q(\sqrt{41}) \)	None	✓	✓	✓	✓	46.4.a.c	$1$	$0$	\(-4\)	\(-1\)	\(10\)	\(6\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-2q^{2}+(1-3\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)
46.4.a.d	$46$	$4$	46.a	1.a	$1$	$2$	$2$	$2.714$	\(\Q(\sqrt{73}) \)	None	✓	✓	✓	✓	46.4.a.d	$1$	$0$	\(4\)	\(3\)	\(10\)	\(12\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+2q^{2}+(2-\beta )q^{3}+4q^{4}+(4+2\beta )q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(46))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(46)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)