Newform orbit 2075.4.a.i

• Label: 2075.4.a.i
• Level: $2075$
• Weight: $4$
• Character orbit: 2075.a
• Self dual: yes
• Analytic conductor: $122.429$
• Analytic rank: $1$
• Dimension: $34$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2075 = 5^{2} \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2075.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(122.428963262\)
Analytic rank:	\(1\)
Dimension:	\(34\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 3 q^{2} - 13 q^{3} + 101 q^{4} - 67 q^{6} - 6 q^{7} + 39 q^{8} + 185 q^{9}+O(q^{10}) \)

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	−5.42383			5.53043			21.4179				0		−29.9961			−1.65460			−72.7765			3.58561				0
1.2	−5.01705			−4.83484			17.1708				0		24.2566			20.3406			−46.0103			−3.62430				0
1.3	−4.93249			4.46910			16.3294				0		−22.0438			23.5481			−41.0847			−7.02714				0
1.4	−4.44928			−0.163709			11.7961				0		0.728385			−28.7776			−16.8897			−26.9732				0
1.5	−3.94871			−3.70791			7.59227				0		14.6415			−2.81080			1.61000			−13.2514				0
1.6	−3.94135			−5.35192			7.53421				0		21.0938			7.99436			1.83586			1.64305				0
1.7	−3.57348			−8.23840			4.76978				0		29.4398			1.02612			11.5431			40.8712				0
1.8	−3.45764			8.07523			3.95530				0		−27.9213			11.2336			13.9851			38.2094				0
1.9	−3.26422			4.41088			2.65514				0		−14.3981			−16.4457			17.4468			−7.54412				0
1.10	−2.48750			7.25084			−1.81235				0		−18.0365			−34.4757			24.4082			25.5747				0
1.11	−2.23569			4.18109			−3.00171				0		−9.34761			−0.426581			24.5964			−9.51848				0
1.12	−2.01995			−3.37599			−3.91979				0		6.81933			14.3579			24.0774			−15.6027				0
1.13	−1.82227			−9.53818			−4.67933				0		17.3811			−0.798852			23.1052			63.9769				0
1.14	−1.40049			−4.17376			−6.03864				0		5.84530			−28.3823			19.6609			−9.57971				0
1.15	−1.39761			6.04029			−6.04670				0		−8.44194			32.8637			19.6317			9.48507				0
1.16	−0.789246			9.45690			−7.37709				0		−7.46383			−18.2639			12.1363			62.4330				0
1.17	−0.686004			−7.54351			−7.52940				0		5.17488			17.6399			10.6532			29.9045				0
1.18	−0.414937			0.693998			−7.82783				0		−0.287965			26.3265			6.56754			−26.5184				0
1.19	0.534288			−1.96221			−7.71454				0		−1.04839			14.0793			−8.39609			−23.1497				0
1.20	0.888352			1.08423			−7.21083				0		0.963180			−15.0559			−13.5126			−25.8244				0

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\( +1 \)
\(83\)	\( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2075.4.a.i	✓	34
5.b	even	2	1		2075.4.a.j	yes	34

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
2075.4.a.i	✓	34	1.a	even	1	1	trivial
2075.4.a.j	yes	34	5.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^34 + 3*T2^33 - 182*T2^32 - 552*T2^31 + 14831*T2^30 + 45661*T2^29 - 714525*T2^28 - 2243571*T2^27 + 22633289*T2^26 + 72897378*T2^25 - 495808088*T2^24 - 1650320600*T2^23 + 7689665394*T2^22 + 26728836174*T2^21 - 84937497350*T2^20 - 313154501974*T2^19 + 661929765935*T2^18 + 2654456073483*T2^17 - 3537999612866*T2^16 - 16134216454520*T2^15 + 12172954959111*T2^14 + 69089601901429*T2^13 - 22628477023669*T2^12 - 202873120862783*T2^11 + 3639010944079*T2^10 + 393064076489744*T2^9 + 77731215701224*T2^8 - 476200044242816*T2^7 - 160384693120560*T2^6 + 334195209736672*T2^5 + 138966262951616*T2^4 - 119359832514816*T2^3 - 54074819895552*T2^2 + 15853097800704*T2 + 7225372704768