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

• Label: 145.2.t
• Level: $145$
• Weight: $2$
• Character orbit: 145.t
• Rep. character: $\chi_{145}(3,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $156$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.t (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{28})\)
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	204	204	0
Cusp forms	156	156	0
Eisenstein series	48	48	0

Trace form

156 * q - 14 * q^2 - 10 * q^3 + 22 * q^4 - 14 * q^5 - 28 * q^6 - 10 * q^7 - 14 * q^8 - 10 * q^9 - 6 * q^10 - 20 * q^11 - 20 * q^12 - 28 * q^13 - 4 * q^14 - 4 * q^15 - 34 * q^16 + 84 * q^18 + 6 * q^20 - 16 * q^21 - 22 * q^22 - 10 * q^23 - 56 * q^24 - 108 * q^25 + 36 * q^26 + 32 * q^27 - 8 * q^28 - 44 * q^30 - 8 * q^31 - 14 * q^32 - 14 * q^33 + 24 * q^34 + 26 * q^35 + 78 * q^36 - 72 * q^37 - 120 * q^38 - 16 * q^39 - 46 * q^40 - 22 * q^41 - 18 * q^42 + 2 * q^43 + 112 * q^44 + 30 * q^45 + 4 * q^46 + 22 * q^47 + 38 * q^48 - 84 * q^49 - 24 * q^50 - 28 * q^51 + 86 * q^52 + 56 * q^53 - 60 * q^55 + 4 * q^56 - 12 * q^57 + 96 * q^58 + 14 * q^60 - 46 * q^61 - 112 * q^62 + 158 * q^63 + 30 * q^64 + 4 * q^65 - 48 * q^66 + 18 * q^67 + 140 * q^68 + 124 * q^69 + 94 * q^70 - 28 * q^71 - 98 * q^72 - 84 * q^73 - 112 * q^74 + 54 * q^75 - 48 * q^76 + 28 * q^77 + 70 * q^78 + 4 * q^79 + 170 * q^80 + 58 * q^81 + 16 * q^82 + 46 * q^83 - 120 * q^84 + 76 * q^85 + 68 * q^87 + 40 * q^88 - 46 * q^89 + 120 * q^90 - 28 * q^91 - 14 * q^92 - 22 * q^93 + 84 * q^94 + 190 * q^95 - 28 * q^96 - 76 * q^97 - 160 * q^98 - 76 * q^99

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.t.a	$145$	$2$	145.t	145.t	$28$	$156$	$13$	$1.158$		None		✓	✓	✓	145.2.o.a	$2$	$0$	\(-14\)	\(-10\)	\(-14\)	\(-10\)		$\mathrm{SU}(2)[C_{28}]$