Properties

Label 6003.2.a.w
Level 6003
Weight 2
Character orbit 6003.a
Self dual Yes
Analytic conductor 47.934
Analytic rank 0
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(0\)
Dimension: \(30\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \(30q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 37q^{4} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(30q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut 37q^{4} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 25q^{22} \) \(\mathstrut -\mathstrut 30q^{23} \) \(\mathstrut +\mathstrut 56q^{25} \) \(\mathstrut +\mathstrut 11q^{26} \) \(\mathstrut +\mathstrut 27q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut +\mathstrut 14q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut +\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 40q^{37} \) \(\mathstrut +\mathstrut 6q^{38} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut +\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 34q^{43} \) \(\mathstrut +\mathstrut 5q^{44} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut -\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 74q^{49} \) \(\mathstrut -\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 71q^{52} \) \(\mathstrut +\mathstrut 16q^{53} \) \(\mathstrut +\mathstrut 22q^{55} \) \(\mathstrut +\mathstrut 14q^{56} \) \(\mathstrut +\mathstrut q^{58} \) \(\mathstrut -\mathstrut 32q^{59} \) \(\mathstrut +\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut +\mathstrut 68q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 27q^{68} \) \(\mathstrut -\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 50q^{73} \) \(\mathstrut -\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 56q^{76} \) \(\mathstrut +\mathstrut 34q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 38q^{82} \) \(\mathstrut -\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 10q^{86} \) \(\mathstrut +\mathstrut 40q^{88} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 37q^{92} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut -\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut 56q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.64113 0 4.97557 −1.42245 0 2.00224 −7.85888 0 3.75688
1.2 −2.60906 0 4.80718 3.69173 0 1.51238 −7.32410 0 −9.63193
1.3 −2.60849 0 4.80424 −1.19758 0 −4.49655 −7.31485 0 3.12388
1.4 −2.55489 0 4.52748 −3.88186 0 2.95370 −6.45744 0 9.91773
1.5 −2.23657 0 3.00224 −0.453557 0 2.23602 −2.24159 0 1.01441
1.6 −1.79065 0 1.20642 3.95479 0 −4.84424 1.42102 0 −7.08163
1.7 −1.59749 0 0.551985 2.02263 0 −1.90895 2.31319 0 −3.23113
1.8 −1.59580 0 0.546582 1.23722 0 2.46504 2.31937 0 −1.97436
1.9 −1.56095 0 0.436554 −3.73116 0 −1.31733 2.44046 0 5.82414
1.10 −1.20001 0 −0.559985 3.40098 0 4.71373 3.07200 0 −4.08120
1.11 −1.12036 0 −0.744798 −4.16877 0 2.81319 3.07516 0 4.67051
1.12 −0.619961 0 −1.61565 −0.522930 0 −1.16804 2.24156 0 0.324196
1.13 −0.534050 0 −1.71479 −2.64563 0 −5.04348 1.98388 0 1.41290
1.14 −0.480943 0 −1.76869 −1.51137 0 3.82960 1.81253 0 0.726880
1.15 −0.395940 0 −1.84323 0.579308 0 −2.59556 1.52169 0 −0.229371
1.16 0.0795257 0 −1.99368 3.50033 0 0.586662 −0.317600 0 0.278366
1.17 0.473233 0 −1.77605 −1.04483 0 3.83278 −1.78695 0 −0.494446
1.18 0.784780 0 −1.38412 2.15464 0 −2.00724 −2.65579 0 1.69092
1.19 0.809520 0 −1.34468 2.87436 0 0.883619 −2.70758 0 2.32685
1.20 0.959410 0 −1.07953 −2.76105 0 2.95320 −2.95453 0 −2.64898
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(23\) \(1\)
\(29\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6003))\):

\(T_{2}^{30} - \cdots\)
\(T_{5}^{30} - \cdots\)