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

• Label: 145.2.m
• Level: $145$
• Weight: $2$
• Character orbit: 145.m
• Rep. character: $\chi_{145}(6,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 145 = 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	145.m (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
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	108	60	48
Cusp forms	84	60	24
Eisenstein series	24	0	24

Trace form

60 * q + 6 * q^4 - 2 * q^5 + 2 * q^6 + 4 * q^7 - 42 * q^8 + 10 * q^9 - 28 * q^11 - 4 * q^13 - 50 * q^16 + 6 * q^20 - 2 * q^22 - 8 * q^23 - 6 * q^24 - 10 * q^25 + 42 * q^27 + 16 * q^28 + 20 * q^29 - 20 * q^30 + 14 * q^31 - 14 * q^32 - 16 * q^33 + 4 * q^34 - 4 * q^35 + 44 * q^36 + 14 * q^37 - 4 * q^38 - 70 * q^39 - 114 * q^42 - 42 * q^44 + 18 * q^45 - 42 * q^48 + 12 * q^49 + 28 * q^51 + 116 * q^52 - 28 * q^53 + 82 * q^54 - 28 * q^55 + 84 * q^56 - 56 * q^57 - 28 * q^58 + 20 * q^59 + 56 * q^61 + 58 * q^62 - 96 * q^63 + 16 * q^64 - 2 * q^65 + 28 * q^66 + 48 * q^67 - 84 * q^68 + 18 * q^71 + 28 * q^73 + 14 * q^74 - 140 * q^76 + 42 * q^77 + 120 * q^78 - 112 * q^79 - 30 * q^80 - 60 * q^81 + 18 * q^82 + 36 * q^83 + 168 * q^84 - 16 * q^86 + 46 * q^87 + 108 * q^88 - 28 * q^89 - 126 * q^90 + 6 * q^91 + 86 * q^92 - 88 * q^93 - 50 * q^94 - 74 * q^96 + 28 * q^97 + 182 * q^98

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.m.a	$145$	$2$	145.m	29.e	$14$	$24$	$4$	$1.158$		None		✓			145.2.m.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(4\)		$\mathrm{SU}(2)[C_{14}]$
145.2.m.b	$145$	$2$	145.m	29.e	$14$	$36$	$6$	$1.158$		None		✓	✓		145.2.m.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$

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

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