Properties

Label 4012.2.b.b
Level 4012
Weight 2
Character orbit 4012.b
Analytic conductor 32.036
Analytic rank 0
Dimension 46
CM No

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(32.0359812909\)
Analytic rank: \(0\)
Dimension: \(46\)
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.

\(\operatorname{Tr}(f)(q) = \) \(46q \) \(\mathstrut -\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(46q \) \(\mathstrut -\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 54q^{25} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 26q^{35} \) \(\mathstrut -\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 66q^{49} \) \(\mathstrut +\mathstrut 26q^{51} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut +\mathstrut 48q^{67} \) \(\mathstrut +\mathstrut 28q^{69} \) \(\mathstrut +\mathstrut 22q^{77} \) \(\mathstrut +\mathstrut 70q^{81} \) \(\mathstrut -\mathstrut 52q^{83} \) \(\mathstrut -\mathstrut 2q^{85} \) \(\mathstrut +\mathstrut 44q^{87} \) \(\mathstrut -\mathstrut 76q^{89} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
237.1 0 3.24132i 0 0.276658i 0 5.07344i 0 −7.50616 0
237.2 0 3.20235i 0 1.49915i 0 2.89750i 0 −7.25507 0
237.3 0 3.18403i 0 1.45906i 0 1.23253i 0 −7.13805 0
237.4 0 3.13247i 0 3.91603i 0 2.98385i 0 −6.81236 0
237.5 0 2.81557i 0 1.77357i 0 1.01302i 0 −4.92746 0
237.6 0 2.74502i 0 1.20235i 0 3.93843i 0 −4.53516 0
237.7 0 2.57223i 0 2.31913i 0 3.71324i 0 −3.61638 0
237.8 0 2.34087i 0 2.91532i 0 3.43927i 0 −2.47969 0
237.9 0 2.27623i 0 2.55864i 0 1.00518i 0 −2.18122 0
237.10 0 1.82354i 0 0.284793i 0 0.645277i 0 −0.325298 0
237.11 0 1.79340i 0 1.19915i 0 1.20458i 0 −0.216279 0
237.12 0 1.77972i 0 1.91545i 0 2.45686i 0 −0.167415 0
237.13 0 1.58213i 0 3.58424i 0 1.89303i 0 0.496852 0
237.14 0 1.50352i 0 4.31120i 0 4.93216i 0 0.739426 0
237.15 0 1.45665i 0 3.69601i 0 3.33013i 0 0.878183 0
237.16 0 1.43806i 0 2.66437i 0 3.93282i 0 0.931993 0
237.17 0 1.38906i 0 2.35139i 0 0.244801i 0 1.07052 0
237.18 0 1.13278i 0 2.09684i 0 2.71039i 0 1.71682 0
237.19 0 0.593296i 0 3.87533i 0 2.92807i 0 2.64800 0
237.20 0 0.405081i 0 1.20499i 0 0.122460i 0 2.83591 0
See all 46 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 237.46
Significant digits:
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Inner twists

This newform does not have CM; other inner twists have not been computed.