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

• Label: 145.2.b
• Level: $145$
• Weight: $2$
• Character orbit: 145.b
• Rep. character: $\chi_{145}(59,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $3$
• Sturm bound: $30$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(30\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	18	14	4
Cusp forms	14	14	0
Eisenstein series	4	0	4

Trace form

14 * q - 18 * q^4 + 4 * q^6 - 10 * q^9 + 2 * q^10 - 8 * q^11 + 8 * q^14 - 2 * q^15 + 18 * q^16 - 12 * q^19 + 4 * q^20 - 28 * q^24 + 16 * q^25 - 4 * q^26 + 6 * q^29 + 34 * q^30 - 8 * q^31 - 28 * q^34 + 8 * q^35 - 10 * q^36 + 36 * q^39 + 34 * q^40 + 4 * q^41 - 26 * q^45 - 40 * q^46 - 22 * q^49 + 14 * q^50 + 24 * q^51 - 20 * q^54 - 26 * q^55 + 16 * q^56 - 40 * q^59 + 26 * q^60 + 20 * q^61 - 26 * q^64 + 18 * q^65 + 4 * q^66 + 32 * q^69 + 48 * q^70 + 16 * q^71 + 4 * q^74 - 6 * q^75 - 20 * q^76 - 40 * q^79 - 64 * q^80 - 18 * q^81 + 40 * q^84 - 20 * q^85 - 36 * q^86 + 12 * q^89 - 24 * q^90 + 56 * q^91 + 20 * q^94 - 4 * q^95 + 28 * q^96 - 68 * 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.b.a	$145$	$2$	145.b	5.b	$2$	$4$	$4$	$1.158$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓			145.2.b.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
145.2.b.b	$145$	$2$	145.b	5.b	$2$	$4$	$4$	$1.158$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			145.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
145.2.b.c	$145$	$2$	145.b	5.b	$2$	$6$	$6$	$1.158$	6.0.84345856.2	None		✓	✓		145.2.b.c	$2$	$0$	\(0\)	\(0\)	\(3\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{5})q^{3}+(-3+\beta _{3}+\cdots)q^{4}+\cdots\)