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

• Label: 145.2.c
• Level: $145$
• Weight: $2$
• Character orbit: 145.c
• Rep. character: $\chi_{145}(86,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(1\)
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	10	8
Cusp forms	14	10	4
Eisenstein series	4	0	4

Trace form

10 * q - 6 * q^4 + 2 * q^5 - 16 * q^6 - 4 * q^7 - 10 * q^9 + 4 * q^13 + 22 * q^16 - 6 * q^20 + 16 * q^22 - 20 * q^23 + 48 * q^24 + 10 * q^25 - 44 * q^28 - 6 * q^29 - 8 * q^30 + 16 * q^33 - 4 * q^34 + 4 * q^35 - 2 * q^36 + 32 * q^38 - 40 * q^42 - 18 * q^45 + 2 * q^49 - 4 * q^52 + 28 * q^53 - 40 * q^54 + 56 * q^57 + 8 * q^59 + 40 * q^62 + 12 * q^63 - 30 * q^64 - 12 * q^65 - 20 * q^67 - 32 * q^71 + 28 * q^74 - 8 * q^78 + 30 * q^80 + 18 * q^81 - 88 * q^82 - 36 * q^83 + 16 * q^86 + 24 * q^87 - 24 * q^88 - 48 * q^91 + 12 * q^92 - 24 * q^93 + 64 * q^94 - 24 * 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.c.a	$145$	$2$	145.c	29.b	$2$	$4$	$4$	$1.158$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			145.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{3})q^{3}+\beta _{2}q^{4}-q^{5}+\cdots\)
145.2.c.b	$145$	$2$	145.c	29.b	$2$	$6$	$6$	$1.158$	6.0.16516096.1	None		✓	✓		145.2.c.b	$2$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(145, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(145, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)