Properties

Label 672.2.bb.a
Level 672
Weight 2
Character orbit 672.bb
Analytic conductor 5.366
Analytic rank 0
Dimension 32
CM No

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Newspace parameters

Level: \( N \) = \( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 672.bb (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(5.36594701583\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32q + 16q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q + 16q^{9} - 8q^{11} - 16q^{25} + 24q^{35} + 16q^{43} + 8q^{49} + 16q^{57} + 96q^{59} + 32q^{67} - 24q^{73} - 16q^{81} - 56q^{91} - 16q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
271.1 0 −0.866025 + 0.500000i 0 −2.08776 + 3.61611i 0 −2.39694 + 1.12013i 0 0.500000 0.866025i 0
271.2 0 −0.866025 + 0.500000i 0 −1.25150 + 2.16767i 0 1.36321 2.26752i 0 0.500000 0.866025i 0
271.3 0 −0.866025 + 0.500000i 0 −0.225540 + 0.390646i 0 −0.458196 2.60577i 0 0.500000 0.866025i 0
271.4 0 −0.866025 + 0.500000i 0 −0.155280 + 0.268953i 0 2.58581 + 0.560001i 0 0.500000 0.866025i 0
271.5 0 −0.866025 + 0.500000i 0 0.155280 0.268953i 0 −2.58581 0.560001i 0 0.500000 0.866025i 0
271.6 0 −0.866025 + 0.500000i 0 0.225540 0.390646i 0 0.458196 + 2.60577i 0 0.500000 0.866025i 0
271.7 0 −0.866025 + 0.500000i 0 1.25150 2.16767i 0 −1.36321 + 2.26752i 0 0.500000 0.866025i 0
271.8 0 −0.866025 + 0.500000i 0 2.08776 3.61611i 0 2.39694 1.12013i 0 0.500000 0.866025i 0
271.9 0 0.866025 0.500000i 0 −1.61398 + 2.79550i 0 1.82725 + 1.91341i 0 0.500000 0.866025i 0
271.10 0 0.866025 0.500000i 0 −1.44142 + 2.49662i 0 −2.63862 + 0.194181i 0 0.500000 0.866025i 0
271.11 0 0.866025 0.500000i 0 −1.14053 + 1.97545i 0 −1.95181 1.78618i 0 0.500000 0.866025i 0
271.12 0 0.866025 0.500000i 0 −0.128707 + 0.222928i 0 0.623918 2.57113i 0 0.500000 0.866025i 0
271.13 0 0.866025 0.500000i 0 0.128707 0.222928i 0 −0.623918 + 2.57113i 0 0.500000 0.866025i 0
271.14 0 0.866025 0.500000i 0 1.14053 1.97545i 0 1.95181 + 1.78618i 0 0.500000 0.866025i 0
271.15 0 0.866025 0.500000i 0 1.44142 2.49662i 0 2.63862 0.194181i 0 0.500000 0.866025i 0
271.16 0 0.866025 0.500000i 0 1.61398 2.79550i 0 −1.82725 1.91341i 0 0.500000 0.866025i 0
367.1 0 −0.866025 0.500000i 0 −2.08776 3.61611i 0 −2.39694 1.12013i 0 0.500000 + 0.866025i 0
367.2 0 −0.866025 0.500000i 0 −1.25150 2.16767i 0 1.36321 + 2.26752i 0 0.500000 + 0.866025i 0
367.3 0 −0.866025 0.500000i 0 −0.225540 0.390646i 0 −0.458196 + 2.60577i 0 0.500000 + 0.866025i 0
367.4 0 −0.866025 0.500000i 0 −0.155280 0.268953i 0 2.58581 0.560001i 0 0.500000 + 0.866025i 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 367.16
Significant digits:
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Inner twists

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

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(672, [\chi])\).