Newform orbit 4805.2.a.bb

• Label: 4805.2.a.bb
• Level: $4805$
• Weight: $2$
• Character orbit: 4805.a
• Self dual: yes
• Analytic conductor: $38.368$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4805 = 5 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4805.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(38.3681181712\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	yes
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) 24 * q + 32 * q^4 - 24 * q^5 + 8 * q^7 + 40 * q^9 + 8 * q^14 + 88 * q^16 - 64 * q^18 + 40 * q^19 - 32 * q^20 + 24 * q^25 + 72 * q^28 + 56 * q^33 - 8 * q^35 + 88 * q^36 - 72 * q^38 + 64 * q^39 - 56 * q^41 - 40 * q^45 - 32 * q^47 + 56 * q^49 + 88 * q^51 + 104 * q^56 + 8 * q^59 + 56 * q^63 + 160 * q^64 - 8 * q^66 + 96 * q^67 + 8 * q^69 - 8 * q^70 - 64 * q^71 - 120 * q^72 + 128 * q^76 - 128 * q^78 - 88 * q^80 + 72 * q^81 + 32 * q^82 - 32 * q^87 + 64 * q^90 + 56 * q^94 - 40 * q^95 + 48 * q^97 - 8 * q^98

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
1.1	−2.67486			−2.55190			5.15485			−1.00000			6.82596			−3.25192			−8.43878			3.51219			2.67486
1.2	−2.67486			2.55190			5.15485			−1.00000			−6.82596			−3.25192			−8.43878			3.51219			2.67486
1.3	−2.66573			−2.65868			5.10611			−1.00000			7.08731			4.70911			−8.28004			4.06856			2.66573
1.4	−2.66573			2.65868			5.10611			−1.00000			−7.08731			4.70911			−8.28004			4.06856			2.66573
1.5	−1.95673			−3.36901			1.82879			−1.00000			6.59224			1.01127			0.335006			8.35023			1.95673
1.6	−1.95673			3.36901			1.82879			−1.00000			−6.59224			1.01127			0.335006			8.35023			1.95673
1.7	−1.14368			−0.176920			−0.692003			−1.00000			0.202339			−1.26713			3.07878			−2.96870			1.14368
1.8	−1.14368			0.176920			−0.692003			−1.00000			−0.202339			−1.26713			3.07878			−2.96870			1.14368
1.9	−0.674641			−0.608276			−1.54486			−1.00000			0.410368			−0.249886			2.39151			−2.63000			0.674641
1.10	−0.674641			0.608276			−1.54486			−1.00000			−0.410368			−0.249886			2.39151			−2.63000			0.674641
1.11	−0.117497			−2.06650			−1.98619			−1.00000			0.242807			4.77107			0.468364			1.27044			0.117497
1.12	−0.117497			2.06650			−1.98619			−1.00000			−0.242807			4.77107			0.468364			1.27044			0.117497
1.13	−0.109488			−3.27311			−1.98801			−1.00000			0.358365			−3.10127			0.436639			7.71323			0.109488
1.14	−0.109488			3.27311			−1.98801			−1.00000			−0.358365			−3.10127			0.436639			7.71323			0.109488
1.15	0.803114			−2.46454			−1.35501			−1.00000			−1.97931			1.24052			−2.69445			3.07398			−0.803114
1.16	0.803114			2.46454			−1.35501			−1.00000			1.97931			1.24052			−2.69445			3.07398			−0.803114
1.17	1.43563			−1.06814			0.0610318			−1.00000			−1.53345			−3.78195			−2.78364			−1.85907			−1.43563
1.18	1.43563			1.06814			0.0610318			−1.00000			1.53345			−3.78195			−2.78364			−1.85907			−1.43563
1.19	1.75387			−0.587870			1.07606			−1.00000			−1.03105			−2.62378			−1.62047			−2.65441			−1.75387
1.20	1.75387			0.587870			1.07606			−1.00000			1.03105			−2.62378			−1.62047			−2.65441			−1.75387

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\( +1 \)
\(31\)	\( -1 \)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
31.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4805.2.a.bb	✓	24
31.b	odd	2	1	inner	4805.2.a.bb	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
4805.2.a.bb	✓	24	1.a	even	1	1	trivial
4805.2.a.bb	✓	24	31.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4805))\):

\( T_{2}^{12} - 20T_{2}^{10} + 141T_{2}^{8} - 416T_{2}^{6} - 8T_{2}^{5} + 482T_{2}^{4} + 52T_{2}^{3} - 162T_{2}^{2} - 36T_{2} - 2 \)

T3^24 - 56*T3^22 + 1352*T3^20 - 18452*T3^18 + 156778*T3^16 - 860136*T3^14 + 3056398*T3^12 - 6866900*T3^10 + 9251697*T3^8 - 6848280*T3^6 + 2451884*T3^4 - 352608*T3^2 + 8836