Space of modular forms of level 605, weight 2, and Character 605.e

• Label: 605.2.e
• Level: $605$
• Weight: $2$
• Character orbit: 605.e
• Rep. character: $\chi_{605}(362,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $92$
• Newform subspaces: $3$
• Sturm bound: $132$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(132\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

	Total	New	Old
Modular forms	156	124	32
Cusp forms	108	92	16
Eisenstein series	48	32	16

Trace form

92 * q + 8 * q^3 + 8 * q^5 - 36 * q^12 + 12 * q^15 - 20 * q^16 - 16 * q^20 - 36 * q^23 - 20 * q^25 + 48 * q^26 - 4 * q^27 - 8 * q^31 - 36 * q^36 - 4 * q^37 - 40 * q^38 + 60 * q^42 + 8 * q^45 + 20 * q^47 - 64 * q^48 - 4 * q^53 - 32 * q^56 + 64 * q^58 + 152 * q^60 - 68 * q^67 + 16 * q^70 + 48 * q^71 - 28 * q^75 - 84 * q^78 - 112 * q^80 + 68 * q^81 - 44 * q^82 + 8 * q^86 - 16 * q^91 - 20 * q^92 - 76 * q^93 + 56 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
605.2.e.a	$605$	$2$	605.e	55.e	$4$	$20$	$10$	$4.831$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓			605.2.e.a	$4$	$0$	\(0\)	\(4\)	\(4\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots\)
605.2.e.b	$605$	$2$	605.e	55.e	$4$	$32$	$16$	$4.831$		None					55.2.l.a	$4$	$0$	\(0\)	\(-4\)	\(8\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
605.2.e.c	$605$	$2$	605.e	55.e	$4$	$40$	$20$	$4.831$		None		✓	✓		605.2.e.c	$4$	$0$	\(0\)	\(8\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(605, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)