Properties

Label 23.15.b.b
Level $23$
Weight $15$
Character orbit 23.b
Analytic conductor $28.596$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 15 \)
Character orbit: \([\chi]\) \(=\) 23.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(28.5956626749\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 184 q^{2} - 2160 q^{3} + 134952 q^{4} - 1666320 q^{6} - 6887840 q^{8} + 24850248 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 184 q^{2} - 2160 q^{3} + 134952 q^{4} - 1666320 q^{6} - 6887840 q^{8} + 24850248 q^{9} - 61408584 q^{12} - 75796032 q^{13} + 61604880 q^{16} + 2078422368 q^{18} + 11061310696 q^{23} - 31030771920 q^{24} - 46421538840 q^{25} - 2664699128 q^{26} + 53616275568 q^{27} + 34752122960 q^{29} - 66504561216 q^{31} - 119385530304 q^{32} + 268767587760 q^{35} - 826304812272 q^{36} - 531040317600 q^{39} - 586388906608 q^{41} - 219014904864 q^{46} + 552854704544 q^{47} + 1314198459696 q^{48} - 2682585958584 q^{49} + 1292374320920 q^{50} - 614830645416 q^{52} - 756511540560 q^{54} - 4886166096240 q^{55} - 4069251029352 q^{58} + 17167207160144 q^{59} + 7479493046896 q^{62} + 18607147469856 q^{64} - 1866422538000 q^{69} + 10676769015360 q^{70} + 15000981757712 q^{71} + 5949703969824 q^{72} + 17535136179168 q^{73} - 79533751619520 q^{75} + 53823905395344 q^{77} + 6433358950512 q^{78} + 149774494087944 q^{81} - 27510435600840 q^{82} - 170228194057680 q^{85} - 286575506293872 q^{87} + 133024510658856 q^{92} + 66347882278032 q^{93} - 205878296932464 q^{94} - 211992774994560 q^{95} + 494703018436320 q^{96} - 537018388090408 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1 −241.960 570.908 42160.6 114189.i −138137. 270764.i −6.23690e6 −4.45703e6 2.76291e7i
22.2 −241.960 570.908 42160.6 114189.i −138137. 270764.i −6.23690e6 −4.45703e6 2.76291e7i
22.3 −181.785 3188.39 16661.8 67250.0i −579603. 311198.i −50505.8 5.38289e6 1.22251e7i
22.4 −181.785 3188.39 16661.8 67250.0i −579603. 311198.i −50505.8 5.38289e6 1.22251e7i
22.5 −176.800 −1555.37 14874.1 28617.6i 274989. 1.02277e6i 266944. −2.36379e6 5.05958e6i
22.6 −176.800 −1555.37 14874.1 28617.6i 274989. 1.02277e6i 266944. −2.36379e6 5.05958e6i
22.7 −115.892 −980.720 −2953.11 117312.i 113657. 1.26769e6i 2.24101e6 −3.82116e6 1.35955e7i
22.8 −115.892 −980.720 −2953.11 117312.i 113657. 1.26769e6i 2.24101e6 −3.82116e6 1.35955e7i
22.9 −73.1726 1838.22 −11029.8 72032.6i −134507. 1.03026e6i 2.00594e6 −1.40393e6 5.27081e6i
22.10 −73.1726 1838.22 −11029.8 72032.6i −134507. 1.03026e6i 2.00594e6 −1.40393e6 5.27081e6i
22.11 −54.1371 −3497.25 −13453.2 104018.i 189331. 363656.i 1.61530e6 7.44782e6 5.63123e6i
22.12 −54.1371 −3497.25 −13453.2 104018.i 189331. 363656.i 1.61530e6 7.44782e6 5.63123e6i
22.13 37.1439 4213.49 −15004.3 126427.i 156505. 1.01652e6i −1.16588e6 1.29705e7 4.69598e6i
22.14 37.1439 4213.49 −15004.3 126427.i 156505. 1.01652e6i −1.16588e6 1.29705e7 4.69598e6i
22.15 51.5135 −1848.44 −13730.4 58352.1i −95219.8 395426.i −1.55130e6 −1.36623e6 3.00593e6i
22.16 51.5135 −1848.44 −13730.4 58352.1i −95219.8 395426.i −1.55130e6 −1.36623e6 3.00593e6i
22.17 133.181 −181.571 1353.30 128567.i −24181.9 828509.i −2.00181e6 −4.75000e6 1.71228e7i
22.18 133.181 −181.571 1353.30 128567.i −24181.9 828509.i −2.00181e6 −4.75000e6 1.71228e7i
22.19 137.789 2037.01 2601.83 58362.5i 280678. 1.12900e6i −1.89903e6 −633549. 8.04171e6i
22.20 137.789 2037.01 2601.83 58362.5i 280678. 1.12900e6i −1.89903e6 −633549. 8.04171e6i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 22.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 23.15.b.b 24
23.b odd 2 1 inner 23.15.b.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
23.15.b.b 24 1.a even 1 1 trivial
23.15.b.b 24 23.b odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} + 92 T_{2}^{11} - 127810 T_{2}^{10} - 9865224 T_{2}^{9} + 5912332672 T_{2}^{8} + 366384186880 T_{2}^{7} - 123538605332480 T_{2}^{6} + \cdots + 47\!\cdots\!00 \) acting on \(S_{15}^{\mathrm{new}}(23, [\chi])\). Copy content Toggle raw display