Space of modular forms of level 46, weight 2, and Character 46.c

• Label: 46.2.c
• Level: $46$
• Weight: $2$
• Character orbit: 46.c
• Rep. character: $\chi_{46}(3,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(46, [\chi])\).

	Total	New	Old
Modular forms	80	20	60
Cusp forms	40	20	20
Eisenstein series	40	0	40

Trace form

20 * q - 4 * q^3 - 2 * q^4 - 10 * q^5 - 4 * q^6 - 4 * q^7 - 10 * q^9 - 2 * q^10 - 14 * q^11 - 4 * q^12 - 12 * q^13 - 12 * q^14 - 2 * q^15 - 2 * q^16 + 6 * q^17 + 28 * q^18 + 4 * q^19 + 12 * q^20 + 34 * q^21 + 12 * q^22 + 20 * q^23 - 4 * q^24 + 2 * q^25 + 6 * q^26 + 26 * q^27 + 18 * q^28 - 10 * q^29 + 20 * q^30 - 10 * q^31 - 26 * q^33 - 20 * q^34 - 10 * q^35 - 10 * q^36 + 10 * q^37 - 22 * q^38 - 12 * q^39 - 2 * q^40 - 26 * q^41 - 32 * q^42 - 10 * q^43 - 14 * q^44 - 22 * q^46 - 4 * q^47 - 4 * q^48 - 20 * q^50 - 28 * q^51 - 12 * q^52 - 28 * q^53 - 18 * q^54 + 8 * q^55 + 10 * q^56 + 30 * q^57 + 16 * q^58 + 38 * q^59 - 2 * q^60 + 34 * q^61 + 34 * q^62 - 6 * q^63 - 2 * q^64 + 78 * q^65 + 40 * q^66 - 14 * q^67 + 28 * q^68 + 18 * q^69 + 24 * q^70 + 38 * q^71 + 28 * q^72 - 36 * q^73 + 46 * q^74 + 52 * q^75 - 18 * q^76 + 22 * q^77 + 10 * q^78 + 42 * q^79 + 12 * q^80 + 2 * q^81 + 8 * q^82 - 10 * q^83 - 10 * q^84 - 34 * q^85 - 12 * q^86 - 54 * q^87 - 10 * q^88 - 62 * q^89 - 90 * q^90 - 76 * q^91 - 24 * q^92 - 128 * q^93 - 48 * q^94 - 46 * q^95 - 4 * q^96 - 16 * q^97 - 4 * q^98 + 26 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(46, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
46.2.c.a	$46$	$2$	46.c	23.c	$11$	$10$	$1$	$0.367$	\(\Q(\zeta_{22})\)	None		✓			46.2.c.a	$2$	$0$	\(-1\)	\(-4\)	\(-6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q-\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{7}+\cdots)q^{3}+\cdots\)
46.2.c.b	$46$	$2$	46.c	23.c	$11$	$10$	$1$	$0.367$	\(\Q(\zeta_{22})\)	None		✓			46.2.c.b	$2$	$0$	\(1\)	\(0\)	\(-4\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+\zeta_{22}q^{2}+(-\zeta_{22}+\zeta_{22}^{4}+\zeta_{22}^{7}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(46, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(46, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)