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

• Label: 605.2.u
• Level: $605$
• Weight: $2$
• Character orbit: 605.u
• Rep. character: $\chi_{605}(4,\cdot)$
• Character field: $\Q(\zeta_{110})$
• Dimension: $2560$
• Newform subspaces: $1$
• Sturm bound: $132$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.u (of order \(110\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 605 \)
Character field:			\(\Q(\zeta_{110})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(132\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	2720	2720	0
Cusp forms	2560	2560	0
Eisenstein series	160	160	0

Trace form

2560 * q - 144 * q^4 - 43 * q^5 - 114 * q^6 + 534 * q^9 - 22 * q^10 - 104 * q^11 - 80 * q^14 - 58 * q^15 - 40 * q^16 - 94 * q^19 - 32 * q^20 - 162 * q^21 - 248 * q^24 - 25 * q^25 - 124 * q^26 - 90 * q^29 - 103 * q^30 - 102 * q^31 - 56 * q^34 - 66 * q^35 - 24 * q^36 - 184 * q^39 - 45 * q^40 - 36 * q^41 - 92 * q^44 - 2 * q^45 - 26 * q^46 - 182 * q^49 - 94 * q^50 + 108 * q^51 - 180 * q^54 + 52 * q^55 + 16 * q^56 - 96 * q^59 - 63 * q^60 - 48 * q^61 - 124 * q^64 - 37 * q^65 - 212 * q^66 - 170 * q^69 + 30 * q^70 - 194 * q^71 - 136 * q^74 - 46 * q^75 - 188 * q^76 - 170 * q^79 + 65 * q^80 - 730 * q^81 - 166 * q^84 - 58 * q^85 - 126 * q^86 + 38 * q^89 - 144 * q^90 - 10 * q^91 + 8 * q^94 - 180 * q^95 - 68 * q^96 + 226 * q^99

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.u.a	$605$	$2$	605.u	605.u	$110$	$2560$	$64$	$4.831$		None		✓	✓	✓	605.2.u.a	$4$	$0$	\(0\)	\(0\)	\(-43\)	\(0\)		$\mathrm{SU}(2)[C_{110}]$