Space of modular forms of level 265, weight 2, and Character 265.d

• Label: 265.2.d
• Level: $265$
• Weight: $2$
• Character orbit: 265.d
• Rep. character: $\chi_{265}(264,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $54$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 265 = 5 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	265.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 265 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(54\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(265, [\chi])\).

	Total	New	Old
Modular forms	28	28	0
Cusp forms	24	24	0
Eisenstein series	4	4	0

Trace form

24 * q + 12 * q^4 - 4 * q^6 + 8 * q^9 + 4 * q^10 + 8 * q^11 + 4 * q^15 - 12 * q^16 - 32 * q^24 - 28 * q^25 + 4 * q^29 - 16 * q^36 + 16 * q^40 - 36 * q^44 + 40 * q^46 - 40 * q^49 + 24 * q^54 - 20 * q^59 + 28 * q^60 - 24 * q^64 - 56 * q^66 + 44 * q^69 + 12 * q^70 - 48 * q^81 + 44 * q^89 - 76 * q^90 + 24 * q^91 + 32 * q^95 + 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(265, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
265.2.d.a	$265$	$2$	265.d	265.d	$2$	$4$	$4$	$2.116$	4.0.4400.1	None		✓			265.2.d.a	$2$	$1$	\(-2\)	\(-6\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
265.2.d.b	$265$	$2$	265.d	265.d	$2$	$4$	$4$	$2.116$	4.0.4400.1	None		✓			265.2.d.a	$2$	$0$	\(2\)	\(6\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{2})q^{2}+(2-\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
265.2.d.c	$265$	$2$	265.d	265.d	$2$	$16$	$16$	$2.116$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		265.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{10}q^{2}-\beta _{15}q^{3}+(1+\beta _{1})q^{4}-\beta _{14}q^{5}+\cdots\)