Space of modular forms of level 1305, weight 2, and Character 1305.r

• Label: 1305.2.r
• Level: $1305$
• Weight: $2$
• Character orbit: 1305.r
• Rep. character: $\chi_{1305}(476,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $80$
• Newform subspaces: $4$
• Sturm bound: $360$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 87 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(360\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1305, [\chi])\).

	Total	New	Old
Modular forms	376	80	296
Cusp forms	344	80	264
Eisenstein series	32	0	32

Trace form

\( 80 q - 48 q^{16} + 80 q^{25} + 16 q^{37} + 48 q^{43} - 96 q^{46} + 144 q^{49} + 80 q^{52} - 16 q^{55} + 48 q^{58} + 48 q^{61} + 48 q^{70} - 64 q^{76} - 32 q^{79} - 128 q^{82} + 64 q^{88} - 176 q^{94} - 80 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1305, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1305.2.r.a	$1305$	$2$	1305.r	87.f	$4$	$8$	$4$	$10.420$	8.0.\(\cdots\).11	None		✓			1305.2.r.a	$2$	$0$	\(0\)	\(0\)	\(-8\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{4}q^{4}-q^{5}+(-1+\beta _{3}+\cdots)q^{7}+\cdots\)
1305.2.r.b	$1305$	$2$	1305.r	87.f	$4$	$8$	$4$	$10.420$	8.0.\(\cdots\).11	None		✓			1305.2.r.a	$2$	$0$	\(0\)	\(0\)	\(8\)	\(-8\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{1}q^{2}-\beta _{4}q^{4}+q^{5}+(-1-\beta _{3}+\cdots)q^{7}+\cdots\)
1305.2.r.c	$1305$	$2$	1305.r	87.f	$4$	$32$	$16$	$10.420$		None		✓			1305.2.r.c	$2$	$0$	\(0\)	\(0\)	\(-32\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$
1305.2.r.d	$1305$	$2$	1305.r	87.f	$4$	$32$	$16$	$10.420$		None		✓			1305.2.r.c	$2$	$0$	\(0\)	\(0\)	\(32\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(87, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(261, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)