Properties

Label 483.2.v.a
Level $483$
Weight $2$
Character orbit 483.v
Analytic conductor $3.857$
Analytic rank $0$
Dimension $600$
CM no
Inner twists $8$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.v (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(600\)
Relative dimension: \(60\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 600q + 20q^{4} - 18q^{7} - 26q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 600q + 20q^{4} - 18q^{7} - 26q^{9} - 14q^{15} - 116q^{16} - 46q^{18} - 50q^{21} - 104q^{22} - 88q^{25} - 26q^{28} + 26q^{30} - 26q^{36} - 56q^{37} - 14q^{39} + 5q^{42} - 40q^{43} - 44q^{46} + 74q^{49} + 14q^{51} - 66q^{57} - 76q^{58} + 22q^{60} - 44q^{63} + 44q^{64} - 92q^{67} - 92q^{70} + 178q^{72} - 182q^{78} + 68q^{79} + 106q^{81} - 87q^{84} - 4q^{85} - 220q^{88} - 24q^{91} - 44q^{93} - 250q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
41.1 −0.783018 + 2.66671i −1.29371 + 1.15165i −4.81573 3.09488i 0.328519 2.28490i −2.05813 4.35173i −2.59187 + 0.531216i 7.82307 6.77873i 0.347391 2.97982i 5.83594 + 2.66518i
41.2 −0.783018 + 2.66671i 1.29371 1.15165i −4.81573 3.09488i −0.328519 + 2.28490i 2.05813 + 4.35173i 2.09878 1.61094i 7.82307 6.77873i 0.347391 2.97982i −5.83594 2.66518i
41.3 −0.698454 + 2.37872i −1.39478 1.02693i −3.48795 2.24157i −0.386473 + 2.68798i 3.41696 2.60053i 0.0322339 + 2.64555i 4.02101 3.48422i 0.890837 + 2.86468i −6.12401 2.79674i
41.4 −0.698454 + 2.37872i 1.39478 + 1.02693i −3.48795 2.24157i 0.386473 2.68798i −3.41696 + 2.60053i 1.97827 + 1.75683i 4.02101 3.48422i 0.890837 + 2.86468i 6.12401 + 2.79674i
41.5 −0.688131 + 2.34356i −1.70257 + 0.318198i −3.33623 2.14407i −0.310810 + 2.16173i 0.425877 4.20904i 1.22272 2.34626i 3.62868 3.14427i 2.79750 1.08351i −4.85226 2.21595i
41.6 −0.688131 + 2.34356i 1.70257 0.318198i −3.33623 2.14407i 0.310810 2.16173i −0.425877 + 4.20904i −2.57390 0.612403i 3.62868 3.14427i 2.79750 1.08351i 4.85226 + 2.21595i
41.7 −0.659075 + 2.24460i −0.178359 + 1.72284i −2.92135 1.87744i −0.169901 + 1.18169i −3.74955 1.53583i 2.26497 + 1.36744i 2.60355 2.25599i −2.93638 0.614570i −2.54044 1.16018i
41.8 −0.659075 + 2.24460i 0.178359 1.72284i −2.92135 1.87744i 0.169901 1.18169i 3.74955 + 1.53583i −0.449799 + 2.60724i 2.60355 2.25599i −2.93638 0.614570i 2.54044 + 1.16018i
41.9 −0.601323 + 2.04792i −0.160145 + 1.72463i −2.14987 1.38164i −0.358395 + 2.49269i −3.43560 1.36502i −2.54603 + 0.719520i 0.896135 0.776505i −2.94871 0.552383i −4.88932 2.23288i
41.10 −0.601323 + 2.04792i 0.160145 1.72463i −2.14987 1.38164i 0.358395 2.49269i 3.43560 + 1.36502i 2.21107 1.45298i 0.896135 0.776505i −2.94871 0.552383i 4.88932 + 2.23288i
41.11 −0.549147 + 1.87022i −1.59123 + 0.684091i −1.51367 0.972774i 0.245423 1.70696i −0.405583 3.35163i 2.55196 0.698205i −0.295653 + 0.256185i 2.06404 2.17710i 3.05762 + 1.39637i
41.12 −0.549147 + 1.87022i 1.59123 0.684091i −1.51367 0.972774i −0.245423 + 1.70696i 0.405583 + 3.35163i −2.19885 + 1.47142i −0.295653 + 0.256185i 2.06404 2.17710i −3.05762 1.39637i
41.13 −0.493988 + 1.68237i −0.151912 + 1.72538i −0.903836 0.580860i 0.558871 3.88703i −2.82768 1.10789i −0.0105749 2.64573i −1.22655 + 1.06281i −2.95385 0.524209i 6.26335 + 2.86037i
41.14 −0.493988 + 1.68237i 0.151912 1.72538i −0.903836 0.580860i −0.558871 + 3.88703i 2.82768 + 1.10789i −1.99258 1.74058i −1.22655 + 1.06281i −2.95385 0.524209i −6.26335 2.86037i
41.15 −0.468338 + 1.59501i −1.57515 0.720338i −0.642222 0.412731i 0.0822804 0.572273i 1.88665 2.17503i −1.81311 1.92682i −1.55355 + 1.34616i 1.96223 + 2.26929i 0.874248 + 0.399256i
41.16 −0.468338 + 1.59501i 1.57515 + 0.720338i −0.642222 0.412731i −0.0822804 + 0.572273i −1.88665 + 2.17503i −0.268855 2.63206i −1.55355 + 1.34616i 1.96223 + 2.26929i −0.874248 0.399256i
41.17 −0.454217 + 1.54692i −1.66392 0.481000i −0.504143 0.323993i 0.562316 3.91099i 1.49985 2.35548i −1.48783 + 2.18778i −1.70670 + 1.47886i 2.53728 + 1.60069i 5.79458 + 2.64630i
41.18 −0.454217 + 1.54692i 1.66392 + 0.481000i −0.504143 0.323993i −0.562316 + 3.91099i −1.49985 + 2.35548i 2.62773 + 0.308264i −1.70670 + 1.47886i 2.53728 + 1.60069i −5.79458 2.64630i
41.19 −0.340118 + 1.15833i −1.07735 1.35621i 0.456447 + 0.293341i −0.0646472 + 0.449631i 1.93738 0.786663i 2.56225 + 0.659450i −2.31977 + 2.01009i −0.678624 + 2.92224i −0.498836 0.227811i
41.20 −0.340118 + 1.15833i 1.07735 + 1.35621i 0.456447 + 0.293341i 0.0646472 0.449631i −1.93738 + 0.786663i −1.17954 + 2.36827i −2.31977 + 2.01009i −0.678624 + 2.92224i 0.498836 + 0.227811i
See next 80 embeddings (of 600 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 440.60
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.b odd 2 1 inner
21.c even 2 1 inner
23.c even 11 1 inner
69.h odd 22 1 inner
161.l odd 22 1 inner
483.v even 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.v.a 600
3.b odd 2 1 inner 483.2.v.a 600
7.b odd 2 1 inner 483.2.v.a 600
21.c even 2 1 inner 483.2.v.a 600
23.c even 11 1 inner 483.2.v.a 600
69.h odd 22 1 inner 483.2.v.a 600
161.l odd 22 1 inner 483.2.v.a 600
483.v even 22 1 inner 483.2.v.a 600
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.v.a 600 1.a even 1 1 trivial
483.2.v.a 600 3.b odd 2 1 inner
483.2.v.a 600 7.b odd 2 1 inner
483.2.v.a 600 21.c even 2 1 inner
483.2.v.a 600 23.c even 11 1 inner
483.2.v.a 600 69.h odd 22 1 inner
483.2.v.a 600 161.l odd 22 1 inner
483.2.v.a 600 483.v even 22 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(483, [\chi])\).