Space of modular forms of level 1305, weight 1, and Character 1305.o

• Label: 1305.1.o
• Level: $1305$
• Weight: $1$
• Character orbit: 1305.o
• Rep. character: $\chi_{1305}(28,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1305.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1305, [\chi])\).

	Total	New	Old
Modular forms	24	6	18
Cusp forms	8	2	6
Eisenstein series	16	4	12

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1305, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1305.1.o.a	$1305$	$1$	1305.o	145.h	$4$	$2$	$1$	$0.651$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{29}) \)			✓	✓	145.1.h.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-iq^{4}+iq^{5}+(-1+i)q^{7}+(1+i+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1305, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1305, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(435, [\chi])\)\(^{\oplus 2}\)