Properties

Label 1503.2.c.a
Level $1503$
Weight $2$
Character orbit 1503.c
Analytic conductor $12.002$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1503 = 3^{2} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1503.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0015154238\)
Analytic rank: \(0\)
Dimension: \(56\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 56q - 48q^{4} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 56q - 48q^{4} + 32q^{16} - 8q^{19} + 16q^{22} + 64q^{25} - 32q^{28} + 40q^{31} + 56q^{49} - 32q^{58} + 24q^{61} - 56q^{76} + 72q^{88} - 56q^{94} - 48q^{97} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1502.1 1.18160i 0 0.603817 −4.40626 0 −3.48779 3.07668i 0 5.20644i
1502.2 1.18160i 0 0.603817 −4.40626 0 −3.48779 3.07668i 0 5.20644i
1502.3 2.66906i 0 −5.12388 −3.16492 0 −0.263490 8.33782i 0 8.44736i
1502.4 2.66906i 0 −5.12388 −3.16492 0 −0.263490 8.33782i 0 8.44736i
1502.5 1.78744i 0 −1.19494 3.10541 0 3.91211 1.43899i 0 5.55073i
1502.6 1.78744i 0 −1.19494 3.10541 0 3.91211 1.43899i 0 5.55073i
1502.7 2.52227i 0 −4.36184 2.54201 0 2.74873 5.95720i 0 6.41163i
1502.8 2.52227i 0 −4.36184 2.54201 0 2.74873 5.95720i 0 6.41163i
1502.9 1.78653i 0 −1.19168 3.08210 0 4.41569 1.44408i 0 5.50625i
1502.10 1.78653i 0 −1.19168 3.08210 0 4.41569 1.44408i 0 5.50625i
1502.11 0.118553i 0 1.98595 3.37331 0 2.05489 0.472544i 0 0.399915i
1502.12 0.118553i 0 1.98595 3.37331 0 2.05489 0.472544i 0 0.399915i
1502.13 2.46644i 0 −4.08332 1.88017 0 −1.78260 5.13837i 0 4.63731i
1502.14 2.46644i 0 −4.08332 1.88017 0 −1.78260 5.13837i 0 4.63731i
1502.15 2.16730i 0 −2.69717 −1.88079 0 −3.73517 1.51098i 0 4.07624i
1502.16 2.16730i 0 −2.69717 −1.88079 0 −3.73517 1.51098i 0 4.07624i
1502.17 0.799957i 0 1.36007 −2.53587 0 −2.19364 2.68791i 0 2.02859i
1502.18 0.799957i 0 1.36007 −2.53587 0 −2.19364 2.68791i 0 2.02859i
1502.19 1.84274i 0 −1.39570 −1.15735 0 0.906437 1.11357i 0 2.13270i
1502.20 1.84274i 0 −1.39570 −1.15735 0 0.906437 1.11357i 0 2.13270i
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1502.56
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
167.b odd 2 1 inner
501.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1503.2.c.a 56
3.b odd 2 1 inner 1503.2.c.a 56
167.b odd 2 1 inner 1503.2.c.a 56
501.c even 2 1 inner 1503.2.c.a 56
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1503.2.c.a 56 1.a even 1 1 trivial
1503.2.c.a 56 3.b odd 2 1 inner
1503.2.c.a 56 167.b odd 2 1 inner
1503.2.c.a 56 501.c even 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1503, [\chi])\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database