Properties

Label 600.2.m.e
Level 600
Weight 2
Character orbit 600.m
Analytic conductor 4.791
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 600.m (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(4.79102412128\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut +\mathstrut 14q^{6} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 38q^{36} \) \(\mathstrut -\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 72q^{49} \) \(\mathstrut -\mathstrut 60q^{51} \) \(\mathstrut +\mathstrut 60q^{54} \) \(\mathstrut -\mathstrut 20q^{64} \) \(\mathstrut +\mathstrut 14q^{66} \) \(\mathstrut -\mathstrut 76q^{76} \) \(\mathstrut -\mathstrut 20q^{81} \) \(\mathstrut +\mathstrut 68q^{84} \) \(\mathstrut -\mathstrut 48q^{91} \) \(\mathstrut -\mathstrut 56q^{94} \) \(\mathstrut -\mathstrut 62q^{96} \) \(\mathstrut -\mathstrut 116q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
299.1 −1.13191 0.847808i −1.71500 0.242431i 0.562443 + 1.91929i 0 1.73569 + 1.72840i 3.08957 0.990551 2.64930i 2.88245 + 0.831539i 0
299.2 −1.13191 0.847808i −1.71500 + 0.242431i 0.562443 + 1.91929i 0 2.14676 + 1.17958i −3.08957 0.990551 2.64930i 2.88245 0.831539i 0
299.3 −1.13191 + 0.847808i −1.71500 0.242431i 0.562443 1.91929i 0 2.14676 1.17958i −3.08957 0.990551 + 2.64930i 2.88245 + 0.831539i 0
299.4 −1.13191 + 0.847808i −1.71500 + 0.242431i 0.562443 1.91929i 0 1.73569 1.72840i 3.08957 0.990551 + 2.64930i 2.88245 0.831539i 0
299.5 −0.639662 1.26128i 0.730070 1.57067i −1.18166 + 1.61359i 0 −2.44805 + 0.0838735i 1.25539 2.79106 + 0.458259i −1.93400 2.29339i 0
299.6 −0.639662 1.26128i 0.730070 + 1.57067i −1.18166 + 1.61359i 0 1.51406 1.92552i −1.25539 2.79106 + 0.458259i −1.93400 + 2.29339i 0
299.7 −0.639662 + 1.26128i 0.730070 1.57067i −1.18166 1.61359i 0 1.51406 + 1.92552i −1.25539 2.79106 0.458259i −1.93400 2.29339i 0
299.8 −0.639662 + 1.26128i 0.730070 + 1.57067i −1.18166 1.61359i 0 −2.44805 0.0838735i 1.25539 2.79106 0.458259i −1.93400 + 2.29339i 0
299.9 −0.244153 1.39298i −1.12950 1.31310i −1.88078 + 0.680200i 0 −1.55335 + 1.89397i 4.34495 1.40670 + 2.45381i −0.448458 + 2.96629i 0
299.10 −0.244153 1.39298i −1.12950 + 1.31310i −1.88078 + 0.680200i 0 2.10489 + 1.25277i −4.34495 1.40670 + 2.45381i −0.448458 2.96629i 0
299.11 −0.244153 + 1.39298i −1.12950 1.31310i −1.88078 0.680200i 0 2.10489 1.25277i −4.34495 1.40670 2.45381i −0.448458 + 2.96629i 0
299.12 −0.244153 + 1.39298i −1.12950 + 1.31310i −1.88078 0.680200i 0 −1.55335 1.89397i 4.34495 1.40670 2.45381i −0.448458 2.96629i 0
299.13 0.244153 1.39298i 1.12950 1.31310i −1.88078 0.680200i 0 −1.55335 1.89397i −4.34495 −1.40670 + 2.45381i −0.448458 2.96629i 0
299.14 0.244153 1.39298i 1.12950 + 1.31310i −1.88078 0.680200i 0 2.10489 1.25277i 4.34495 −1.40670 + 2.45381i −0.448458 + 2.96629i 0
299.15 0.244153 + 1.39298i 1.12950 1.31310i −1.88078 + 0.680200i 0 2.10489 + 1.25277i 4.34495 −1.40670 2.45381i −0.448458 2.96629i 0
299.16 0.244153 + 1.39298i 1.12950 + 1.31310i −1.88078 + 0.680200i 0 −1.55335 + 1.89397i −4.34495 −1.40670 2.45381i −0.448458 + 2.96629i 0
299.17 0.639662 1.26128i −0.730070 1.57067i −1.18166 1.61359i 0 −2.44805 0.0838735i −1.25539 −2.79106 + 0.458259i −1.93400 + 2.29339i 0
299.18 0.639662 1.26128i −0.730070 + 1.57067i −1.18166 1.61359i 0 1.51406 + 1.92552i 1.25539 −2.79106 + 0.458259i −1.93400 2.29339i 0
299.19 0.639662 + 1.26128i −0.730070 1.57067i −1.18166 + 1.61359i 0 1.51406 1.92552i 1.25539 −2.79106 0.458259i −1.93400 + 2.29339i 0
299.20 0.639662 + 1.26128i −0.730070 + 1.57067i −1.18166 + 1.61359i 0 −2.44805 + 0.0838735i −1.25539 −2.79106 0.458259i −1.93400 2.29339i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 299.24
Significant digits:
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Inner twists

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

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(600, [\chi])\):

\(T_{7}^{6} \) \(\mathstrut -\mathstrut 30 T_{7}^{4} \) \(\mathstrut +\mathstrut 225 T_{7}^{2} \) \(\mathstrut -\mathstrut 284 \)
\(T_{11}^{6} \) \(\mathstrut +\mathstrut 19 T_{11}^{4} \) \(\mathstrut +\mathstrut 112 T_{11}^{2} \) \(\mathstrut +\mathstrut 200 \)
\(T_{29}^{6} \) \(\mathstrut -\mathstrut 140 T_{29}^{4} \) \(\mathstrut +\mathstrut 5752 T_{29}^{2} \) \(\mathstrut -\mathstrut 56800 \)