Newform orbit 240.3.bn.a

• Label: 240.3.bn.a
• Level: $240$
• Weight: $3$
• Character orbit: 240.bn
• Analytic conductor: $6.540$
• Analytic rank: $0$
• Dimension: $64$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	240.bn (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.53952634465\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 24 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
91.1	−1.99836	−	0.0809611i	1.22474	+	1.22474i	3.98689	+	0.323579i	−1.58114	−	1.58114i	−2.34833	−	2.54664i	−2.50432			−7.94105	−	0.969411i			3.00000i	3.03167	+	3.28770i
91.2	−1.99652	−	0.117912i	−1.22474	−	1.22474i	3.97219	+	0.470829i	−1.58114	−	1.58114i	2.30082	+	2.58964i	12.6948			−7.87505	−	1.40839i			3.00000i	2.97034	+	3.34321i
91.3	−1.88268	+	0.674932i	1.22474	+	1.22474i	3.08893	−	2.54136i	1.58114	+	1.58114i	−3.13242	−	1.47918i	6.93561			−4.10021	+	6.86937i			3.00000i	−4.04393	−	1.90961i
91.4	−1.80521	+	0.860949i	−1.22474	−	1.22474i	2.51753	−	3.10838i	−1.58114	−	1.58114i	3.26536	+	1.15647i	−9.39086			−1.86850	+	7.77873i			3.00000i	4.21556	+	1.49300i
91.5	−1.80387	−	0.863740i	−1.22474	−	1.22474i	2.50791	+	3.11615i	1.58114	+	1.58114i	1.15142	+	3.26714i	0.973675			−1.83240	−	7.78732i			3.00000i	−1.48648	−	4.21786i
91.6	−1.55226	+	1.26115i	1.22474	+	1.22474i	0.818999	−	3.91526i	−1.58114	−	1.58114i	−3.44571	−	0.356530i	−8.42448			3.66643	+	7.11036i			3.00000i	4.44839	+	0.460279i
91.7	−1.36537	−	1.46142i	1.22474	+	1.22474i	−0.271513	+	3.99077i	−1.58114	−	1.58114i	0.117637	−	3.46210i	−2.14501			6.20293	−	5.05210i			3.00000i	−0.151868	+	4.46956i
91.8	−1.26185	−	1.55169i	1.22474	+	1.22474i	−0.815479	+	3.91599i	1.58114	+	1.58114i	0.354982	−	3.44587i	−9.52201			7.10541	−	3.67602i			3.00000i	0.458279	−	4.44859i
91.9	−1.21603	+	1.58785i	1.22474	+	1.22474i	−1.04254	−	3.86175i	1.58114	+	1.58114i	−3.43404	+	0.455383i	−6.89370			7.39964	+	3.04062i			3.00000i	−4.43333	+	0.587897i
91.10	−1.11696	+	1.65904i	−1.22474	−	1.22474i	−1.50481	−	3.70615i	−1.58114	−	1.58114i	3.39989	−	0.663910i	4.00659			7.82945	+	1.64307i			3.00000i	4.38923	−	0.857103i
91.11	−0.979211	+	1.74389i	−1.22474	−	1.22474i	−2.08229	−	3.41527i	1.58114	+	1.58114i	3.33510	−	0.936535i	−6.97297			7.99485	−	0.287019i			3.00000i	−4.30560	+	1.20906i
91.12	−0.823888	−	1.82242i	−1.22474	−	1.22474i	−2.64242	+	3.00294i	1.58114	+	1.58114i	−1.22295	+	3.24105i	2.19624			7.64966	+	2.34151i			3.00000i	1.57882	−	4.18418i
91.13	−0.712831	+	1.86865i	1.22474	+	1.22474i	−2.98374	−	2.66407i	−1.58114	−	1.58114i	−3.16166	+	1.41559i	10.5937			7.10514	−	3.67655i			3.00000i	4.08169	−	1.82752i
91.14	−0.487538	−	1.93967i	−1.22474	−	1.22474i	−3.52461	+	1.89132i	−1.58114	−	1.58114i	−1.77849	+	2.97271i	−0.906944			5.38692	+	5.91449i			3.00000i	−2.29602	+	3.83775i
91.15	−0.319664	−	1.97429i	1.22474	+	1.22474i	−3.79563	+	1.26222i	1.58114	+	1.58114i	2.02649	−	2.80951i	6.96024			3.70531	+	7.09018i			3.00000i	2.61619	−	3.62706i
91.16	0.166064	+	1.99309i	−1.22474	−	1.22474i	−3.94485	+	0.661961i	1.58114	+	1.58114i	2.23765	−	2.64442i	5.18414			−1.97445	−	7.75252i			3.00000i	−2.88879	+	3.41393i
91.17	0.309897	−	1.97585i	1.22474	+	1.22474i	−3.80793	−	1.22462i	−1.58114	−	1.58114i	2.79945	−	2.04036i	−9.60974			−3.59972	+	7.14437i			3.00000i	−3.61408	+	2.63410i
91.18	0.328478	+	1.97284i	−1.22474	−	1.22474i	−3.78420	+	1.29607i	−1.58114	−	1.58114i	2.01393	−	2.81853i	4.74581			−3.79997	−	7.03990i			3.00000i	2.59997	−	3.63871i
91.19	0.405730	−	1.95841i	1.22474	+	1.22474i	−3.67077	−	1.58918i	1.58114	+	1.58114i	2.89547	−	1.90164i	0.712173			−4.60160	+	6.54410i			3.00000i	3.73804	−	2.45501i
91.20	0.446279	+	1.94957i	1.22474	+	1.22474i	−3.60167	+	1.74011i	−1.58114	−	1.58114i	−1.84115	+	2.93431i	−2.37589			−4.99981	−	6.24515i			3.00000i	2.37692	−	3.78817i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
16.f	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	240.3.bn.a	✓	64
4.b	odd	2	1		960.3.bn.a		64
16.e	even	4	1		960.3.bn.a		64
16.f	odd	4	1	inner	240.3.bn.a	✓	64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
240.3.bn.a	✓	64	1.a	even	1	1	trivial
240.3.bn.a	✓	64	16.f	odd	4	1	inner
960.3.bn.a		64	4.b	odd	2	1
960.3.bn.a		64	16.e	even	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(240, [\chi])\).