Space of modular forms of level 145, weight 2, and Character 145.l

• Label: 145.2.l
• Level: $145$
• Weight: $2$
• Character orbit: 145.l
• Rep. character: $\chi_{145}(4,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.l (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(145, [\chi])\).

	Total	New	Old
Modular forms	96	96	0
Cusp forms	72	72	0
Eisenstein series	24	24	0

Trace form

72 * q - 18 * q^4 - 9 * q^5 + 4 * q^6 - 14 * q^9 - 7 * q^10 - 14 * q^11 - 14 * q^14 + 7 * q^15 - 2 * q^16 - 14 * q^19 + 46 * q^20 - 14 * q^21 - 12 * q^24 - 9 * q^25 - 56 * q^26 - 12 * q^29 + 14 * q^30 - 28 * q^31 + 4 * q^34 - 25 * q^35 - 50 * q^36 + 56 * q^40 - 70 * q^44 + 59 * q^45 - 28 * q^49 + 14 * q^50 - 64 * q^51 + 14 * q^54 + 49 * q^55 + 98 * q^56 + 100 * q^59 + 14 * q^60 - 70 * q^61 - 18 * q^64 + 27 * q^65 + 70 * q^66 - 70 * q^69 - 20 * q^71 - 54 * q^74 + 98 * q^76 - 14 * q^79 + 2 * q^80 + 160 * q^81 + 98 * q^84 - 112 * q^85 - 88 * q^86 - 14 * q^89 - 56 * q^90 + 56 * q^91 + 6 * q^94 - 119 * q^95 + 90 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(145, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
145.2.l.a	$145$	$2$	145.l	145.l	$14$	$72$	$12$	$1.158$		None		✓	✓	✓	145.2.l.a	$4$	$0$	\(0\)	\(0\)	\(-9\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$