Newform orbit 935.2.f.a

• Label: 935.2.f.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.f
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $26$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(26\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 26 q + 6 q^{2} + 26 q^{4} + 18 q^{8} - 10 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
441.1	−2.56193				−	0.396689i	4.56346					1.00000i			1.01629i			1.54454i	−6.56740			2.84264				−	2.56193i
441.2	−2.56193					0.396689i	4.56346				−	1.00000i		−	1.01629i		−	1.54454i	−6.56740			2.84264					2.56193i
441.3	−2.20706				−	1.86438i	2.87109				−	1.00000i			4.11478i		−	1.33948i	−1.92255			−0.475904					2.20706i
441.4	−2.20706					1.86438i	2.87109					1.00000i		−	4.11478i			1.33948i	−1.92255			−0.475904				−	2.20706i
441.5	−1.30325				−	2.81017i	−0.301535					1.00000i			3.66236i		−	2.49585i	2.99948			−4.89707				−	1.30325i
441.6	−1.30325					2.81017i	−0.301535				−	1.00000i		−	3.66236i			2.49585i	2.99948			−4.89707					1.30325i
441.7	−1.15651				−	0.439516i	−0.662475					1.00000i			0.508306i			4.98048i	3.07919			2.80683				−	1.15651i
441.8	−1.15651					0.439516i	−0.662475				−	1.00000i		−	0.508306i		−	4.98048i	3.07919			2.80683					1.15651i
441.9	−1.09933				−	0.737686i	−0.791465				−	1.00000i			0.810963i			1.52906i	3.06875			2.45582					1.09933i
441.10	−1.09933					0.737686i	−0.791465					1.00000i		−	0.810963i		−	1.52906i	3.06875			2.45582				−	1.09933i
441.11	−0.0445149				−	3.19424i	−1.99802					1.00000i			0.142191i			0.576540i	0.177971			−7.20317				−	0.0445149i
441.12	−0.0445149					3.19424i	−1.99802				−	1.00000i		−	0.142191i		−	0.576540i	0.177971			−7.20317					0.0445149i
441.13	0.512038				−	1.06186i	−1.73782					1.00000i		−	0.543711i			0.300605i	−1.91390			1.87246					0.512038i
441.14	0.512038					1.06186i	−1.73782				−	1.00000i			0.543711i		−	0.300605i	−1.91390			1.87246				−	0.512038i
441.15	0.791612				−	0.442255i	−1.37335				−	1.00000i		−	0.350095i			0.492618i	−2.67038			2.80441				−	0.791612i
441.16	0.791612					0.442255i	−1.37335					1.00000i			0.350095i		−	0.492618i	−2.67038			2.80441					0.791612i
441.17	0.958418				−	2.70367i	−1.08143				−	1.00000i		−	2.59125i		−	1.13645i	−2.95330			−4.30983				−	0.958418i
441.18	0.958418					2.70367i	−1.08143					1.00000i			2.59125i			1.13645i	−2.95330			−4.30983					0.958418i
441.19	1.54410				−	2.23358i	0.384240					1.00000i		−	3.44887i		−	3.57095i	−2.49489			−1.98888					1.54410i
441.20	1.54410					2.23358i	0.384240				−	1.00000i			3.44887i			3.57095i	−2.49489			−1.98888				−	1.54410i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.f.a	✓	26
17.b	even	2	1	inner	935.2.f.a	✓	26

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.f.a	✓	26	1.a	even	1	1	trivial
935.2.f.a	✓	26	17.b	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^13 - 3*T2^12 - 15*T2^11 + 47*T2^10 + 76*T2^9 - 258*T2^8 - 149*T2^7 + 608*T2^6 + 78*T2^5 - 636*T2^4 + 86*T2^3 + 249*T2^2 - 79*T2 - 4