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

• Label: 605.2.k
• Level: $605$
• Weight: $2$
• Character orbit: 605.k
• Rep. character: $\chi_{605}(56,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $440$
• Newform subspaces: $2$
• Sturm bound: $132$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.k (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 121 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(132\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	680	440	240
Cusp forms	640	440	200
Eisenstein series	40	0	40

Trace form

440 * q - 6 * q^2 - 4 * q^3 - 48 * q^4 - 4 * q^6 - 4 * q^7 - 18 * q^8 + 424 * q^9 - 2 * q^10 - 12 * q^11 + 54 * q^12 + 14 * q^13 + 28 * q^14 + 18 * q^15 - 72 * q^16 - 32 * q^17 - 46 * q^18 - 16 * q^19 - 32 * q^21 - 34 * q^22 + 20 * q^23 + 36 * q^24 - 44 * q^25 - 36 * q^26 - 40 * q^27 - 52 * q^28 - 40 * q^29 - 20 * q^30 + 24 * q^31 - 62 * q^32 - 44 * q^33 - 64 * q^34 - 12 * q^35 - 124 * q^36 - 24 * q^37 - 32 * q^38 - 40 * q^39 + 60 * q^40 - 56 * q^41 - 84 * q^42 - 36 * q^43 - 58 * q^44 - 68 * q^46 - 28 * q^47 - 104 * q^48 - 28 * q^49 - 6 * q^50 + 54 * q^51 + 204 * q^52 + 160 * q^53 + 50 * q^54 - 8 * q^55 - 54 * q^56 + 74 * q^57 + 126 * q^58 - 44 * q^59 - 44 * q^60 - 56 * q^61 + 22 * q^62 - 84 * q^63 + 68 * q^64 - 24 * q^65 - 102 * q^66 - 34 * q^67 - 144 * q^68 - 104 * q^69 - 24 * q^70 - 68 * q^71 - 234 * q^72 - 36 * q^73 - 92 * q^74 - 4 * q^75 + 120 * q^76 + 180 * q^77 + 72 * q^78 + 36 * q^79 - 16 * q^80 + 328 * q^81 - 44 * q^82 - 68 * q^83 - 256 * q^84 + 50 * q^85 - 100 * q^86 - 152 * q^87 + 68 * q^88 + 8 * q^89 + 62 * q^90 + 28 * q^91 + 148 * q^92 - 30 * q^93 - 52 * q^94 - 16 * q^95 + 20 * q^96 - 2 * q^97 + 194 * q^98 - 156 * 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.k.a	$605$	$2$	605.k	121.e	$11$	$220$	$22$	$4.831$		None		✓			605.2.k.a	$2$	$0$	\(-4\)	\(-4\)	\(-22\)	\(-8\)		$\mathrm{SU}(2)[C_{11}]$
605.2.k.b	$605$	$2$	605.k	121.e	$11$	$220$	$22$	$4.831$		None		✓			605.2.k.b	$2$	$0$	\(-2\)	\(0\)	\(22\)	\(4\)		$\mathrm{SU}(2)[C_{11}]$

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

\( S_{2}^{\mathrm{old}}(605, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)