Properties

Label 12.14.b.a
Level 12
Weight 14
Character orbit 12.b
Analytic conductor 12.868
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(12.8677114742\)
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.

\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut -\mathstrut 8376q^{4} \) \(\mathstrut -\mathstrut 135720q^{6} \) \(\mathstrut -\mathstrut 327240q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(24q \) \(\mathstrut -\mathstrut 8376q^{4} \) \(\mathstrut -\mathstrut 135720q^{6} \) \(\mathstrut -\mathstrut 327240q^{9} \) \(\mathstrut +\mathstrut 4403568q^{10} \) \(\mathstrut -\mathstrut 139896q^{12} \) \(\mathstrut -\mathstrut 17520048q^{13} \) \(\mathstrut +\mathstrut 41046816q^{16} \) \(\mathstrut -\mathstrut 102153744q^{18} \) \(\mathstrut +\mathstrut 340864272q^{21} \) \(\mathstrut +\mathstrut 401914896q^{22} \) \(\mathstrut +\mathstrut 14766624q^{24} \) \(\mathstrut -\mathstrut 3043252488q^{25} \) \(\mathstrut +\mathstrut 3306349488q^{28} \) \(\mathstrut +\mathstrut 3523891248q^{30} \) \(\mathstrut -\mathstrut 10577805696q^{33} \) \(\mathstrut +\mathstrut 5461322688q^{34} \) \(\mathstrut +\mathstrut 16126437096q^{36} \) \(\mathstrut -\mathstrut 29352930672q^{37} \) \(\mathstrut -\mathstrut 5243368896q^{40} \) \(\mathstrut +\mathstrut 35399300688q^{42} \) \(\mathstrut +\mathstrut 36221734656q^{45} \) \(\mathstrut +\mathstrut 1675946784q^{46} \) \(\mathstrut +\mathstrut 27878547744q^{48} \) \(\mathstrut -\mathstrut 165718477944q^{49} \) \(\mathstrut -\mathstrut 6459860112q^{52} \) \(\mathstrut -\mathstrut 10955701656q^{54} \) \(\mathstrut +\mathstrut 590611321584q^{57} \) \(\mathstrut -\mathstrut 440462601456q^{58} \) \(\mathstrut -\mathstrut 208761511104q^{60} \) \(\mathstrut +\mathstrut 555426186192q^{61} \) \(\mathstrut -\mathstrut 741528997248q^{64} \) \(\mathstrut +\mathstrut 263546293968q^{66} \) \(\mathstrut -\mathstrut 122266973952q^{69} \) \(\mathstrut -\mathstrut 885399371232q^{70} \) \(\mathstrut +\mathstrut 625428177984q^{72} \) \(\mathstrut +\mathstrut 365028975600q^{73} \) \(\mathstrut +\mathstrut 1427271642000q^{76} \) \(\mathstrut +\mathstrut 1481181276240q^{78} \) \(\mathstrut -\mathstrut 2327652239400q^{81} \) \(\mathstrut +\mathstrut 874644720480q^{82} \) \(\mathstrut -\mathstrut 6757787638224q^{84} \) \(\mathstrut -\mathstrut 3308476422144q^{85} \) \(\mathstrut +\mathstrut 11607512359104q^{88} \) \(\mathstrut +\mathstrut 4426488729648q^{90} \) \(\mathstrut -\mathstrut 3971016902448q^{93} \) \(\mathstrut -\mathstrut 3078833939904q^{94} \) \(\mathstrut -\mathstrut 6470779487616q^{96} \) \(\mathstrut -\mathstrut 4159752429648q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
11.1 −89.8019 11.2966i −433.314 + 1185.99i 7936.77 + 2028.92i 24994.7i 52310.1 101609.i 71320.8i −689818. 271859.i −1.21880e6 1.02781e6i −282356. + 2.24457e6i
11.2 −89.8019 + 11.2966i −433.314 1185.99i 7936.77 2028.92i 24994.7i 52310.1 + 101609.i 71320.8i −689818. + 271859.i −1.21880e6 + 1.02781e6i −282356. 2.24457e6i
11.3 −83.2487 35.5199i 1204.82 + 377.813i 5668.68 + 5913.96i 53567.1i −86879.4 74247.3i 133564.i −261847. 693680.i 1.30884e6 + 910390.i 1.90270e6 4.45939e6i
11.4 −83.2487 + 35.5199i 1204.82 377.813i 5668.68 5913.96i 53567.1i −86879.4 + 74247.3i 133564.i −261847. + 693680.i 1.30884e6 910390.i 1.90270e6 + 4.45939e6i
11.5 −63.1407 64.8479i −1256.10 128.555i −218.513 + 8189.09i 1788.84i 70974.7 + 89572.8i 316886.i 544842. 502894.i 1.56127e6 + 322956.i 116003. 112949.i
11.6 −63.1407 + 64.8479i −1256.10 + 128.555i −218.513 8189.09i 1788.84i 70974.7 89572.8i 316886.i 544842. + 502894.i 1.56127e6 322956.i 116003. + 112949.i
11.7 −61.4564 66.4463i 544.543 1139.21i −638.220 + 8167.10i 30890.7i −109162. + 33828.8i 363071.i 581896. 459513.i −1.00127e6 1.24070e6i −2.05257e6 + 1.89843e6i
11.8 −61.4564 + 66.4463i 544.543 + 1139.21i −638.220 8167.10i 30890.7i −109162. 33828.8i 363071.i 581896. + 459513.i −1.00127e6 + 1.24070e6i −2.05257e6 1.89843e6i
11.9 −26.1905 86.6375i 919.540 + 865.314i −6820.12 + 4538.16i 34796.6i 50885.4 102330.i 298175.i 571797. + 472022.i 96786.4 + 1.59138e6i −3.01469e6 + 911338.i
11.10 −26.1905 + 86.6375i 919.540 865.314i −6820.12 4538.16i 34796.6i 50885.4 + 102330.i 298175.i 571797. 472022.i 96786.4 1.59138e6i −3.01469e6 911338.i
11.11 −9.20327 90.0405i −618.744 + 1100.67i −8022.60 + 1657.33i 49220.1i 104800. + 45582.3i 527913.i 223061. + 707106.i −828634. 1.36207e6i 4.43181e6 452986.i
11.12 −9.20327 + 90.0405i −618.744 1100.67i −8022.60 1657.33i 49220.1i 104800. 45582.3i 527913.i 223061. 707106.i −828634. + 1.36207e6i 4.43181e6 + 452986.i
11.13 9.20327 90.0405i 618.744 1100.67i −8022.60 1657.33i 49220.1i −93410.6 65841.9i 527913.i −223061. + 707106.i −828634. 1.36207e6i 4.43181e6 + 452986.i
11.14 9.20327 + 90.0405i 618.744 + 1100.67i −8022.60 + 1657.33i 49220.1i −93410.6 + 65841.9i 527913.i −223061. 707106.i −828634. + 1.36207e6i 4.43181e6 452986.i
11.15 26.1905 86.6375i −919.540 865.314i −6820.12 4538.16i 34796.6i −99051.9 + 57003.7i 298175.i −571797. + 472022.i 96786.4 + 1.59138e6i −3.01469e6 911338.i
11.16 26.1905 + 86.6375i −919.540 + 865.314i −6820.12 + 4538.16i 34796.6i −99051.9 57003.7i 298175.i −571797. 472022.i 96786.4 1.59138e6i −3.01469e6 + 911338.i
11.17 61.4564 66.4463i −544.543 + 1139.21i −638.220 8167.10i 30890.7i 42230.6 + 106195.i 363071.i −581896. 459513.i −1.00127e6 1.24070e6i −2.05257e6 1.89843e6i
11.18 61.4564 + 66.4463i −544.543 1139.21i −638.220 + 8167.10i 30890.7i 42230.6 106195.i 363071.i −581896. + 459513.i −1.00127e6 + 1.24070e6i −2.05257e6 + 1.89843e6i
11.19 63.1407 64.8479i 1256.10 + 128.555i −218.513 8189.09i 1788.84i 87647.7 73338.7i 316886.i −544842. 502894.i 1.56127e6 + 322956.i 116003. + 112949.i
11.20 63.1407 + 64.8479i 1256.10 128.555i −218.513 + 8189.09i 1788.84i 87647.7 + 73338.7i 316886.i −544842. + 502894.i 1.56127e6 322956.i 116003. 112949.i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 11.24
Significant digits:
Format:

Inner twists

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

Hecke kernels

There are no other newforms in \(S_{14}^{\mathrm{new}}(12, [\chi])\).