Properties

Label 430.2.q.c
Level 430
Weight 2
Character orbit 430.q
Analytic conductor 3.434
Analytic rank 0
Dimension 48
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 430.q (of order \(21\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.43356728692\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{21})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48q + 8q^{2} - 7q^{3} - 8q^{4} + 4q^{5} + 7q^{6} - 3q^{7} + 8q^{8} + 13q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 48q + 8q^{2} - 7q^{3} - 8q^{4} + 4q^{5} + 7q^{6} - 3q^{7} + 8q^{8} + 13q^{9} - 4q^{10} + q^{11} + 14q^{12} - 23q^{13} + 24q^{14} - 8q^{16} + 8q^{17} - 20q^{18} - 3q^{19} + 4q^{20} - 8q^{21} - q^{22} + 7q^{23} + 4q^{25} - 19q^{26} + 32q^{27} + 4q^{28} + 30q^{29} + 9q^{31} + 8q^{32} + 39q^{33} - 8q^{34} - 22q^{35} - 29q^{36} - 37q^{37} - 11q^{38} - 52q^{39} - 4q^{40} - 28q^{41} - 6q^{42} + 41q^{43} + 8q^{44} + 2q^{45} - 28q^{46} + 3q^{47} - 41q^{49} + 24q^{50} - 30q^{51} - 9q^{52} - 69q^{53} + 3q^{54} + 10q^{55} - 11q^{56} + 116q^{57} + 5q^{58} + 10q^{59} - 19q^{61} - 93q^{62} + 34q^{63} - 8q^{64} - 3q^{65} - 18q^{66} + 3q^{67} + 8q^{68} + 42q^{69} + 22q^{70} - 36q^{71} + 22q^{72} - 56q^{73} + 9q^{74} - 10q^{76} + 3q^{77} + 45q^{78} + 16q^{79} - 24q^{80} - 19q^{81} + 14q^{82} + 64q^{83} - 8q^{84} - 30q^{85} + 36q^{86} + 78q^{87} - q^{88} - 75q^{89} + 5q^{90} + 5q^{91} + 14q^{92} - 10q^{93} - 45q^{94} - 3q^{95} + 33q^{97} - q^{98} - 11q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 0.900969 0.433884i −2.07183 + 1.41255i 0.623490 0.781831i −0.733052 0.680173i −1.25377 + 2.17160i −0.525199 0.909671i 0.222521 0.974928i 1.20117 3.06053i −0.955573 0.294755i
31.2 0.900969 0.433884i −0.889549 + 0.606484i 0.623490 0.781831i −0.733052 0.680173i −0.538312 + 0.932384i 2.53031 + 4.38263i 0.222521 0.974928i −0.672549 + 1.71363i −0.955573 0.294755i
31.3 0.900969 0.433884i 1.41868 0.967239i 0.623490 0.781831i −0.733052 0.680173i 0.858516 1.48699i −0.475578 0.823725i 0.222521 0.974928i −0.0189247 + 0.0482195i −0.955573 0.294755i
31.4 0.900969 0.433884i 2.49243 1.69931i 0.623490 0.781831i −0.733052 0.680173i 1.50830 2.61245i 0.376122 + 0.651463i 0.222521 0.974928i 2.22854 5.67822i −0.955573 0.294755i
81.1 0.222521 0.974928i −1.65144 0.509401i −0.900969 0.433884i 0.365341 + 0.930874i −0.864108 + 1.49668i 0.201072 + 0.348266i −0.623490 + 0.781831i −0.0109619 0.00747371i 0.988831 0.149042i
81.2 0.222521 0.974928i −1.23079 0.379647i −0.900969 0.433884i 0.365341 + 0.930874i −0.644004 + 1.11545i 1.26969 + 2.19916i −0.623490 + 0.781831i −1.10802 0.755432i 0.988831 0.149042i
81.3 0.222521 0.974928i 0.485771 + 0.149841i −0.900969 0.433884i 0.365341 + 0.930874i 0.254178 0.440249i −2.29038 3.96705i −0.623490 + 0.781831i −2.26519 1.54438i 0.988831 0.149042i
81.4 0.222521 0.974928i 1.95105 + 0.601821i −0.900969 0.433884i 0.365341 + 0.930874i 1.02088 1.76822i 2.34372 + 4.05945i −0.623490 + 0.781831i 0.965710 + 0.658410i 0.988831 0.149042i
101.1 −0.623490 + 0.781831i −1.14663 + 2.92157i −0.222521 0.974928i 0.0747301 + 0.997204i −1.56926 2.71804i −0.830202 + 1.43795i 0.900969 + 0.433884i −5.02164 4.65940i −0.826239 0.563320i
101.2 −0.623490 + 0.781831i −0.399818 + 1.01872i −0.222521 0.974928i 0.0747301 + 0.997204i −0.547184 0.947751i 0.630880 1.09272i 0.900969 + 0.433884i 1.32122 + 1.22591i −0.826239 0.563320i
101.3 −0.623490 + 0.781831i 0.396839 1.01113i −0.222521 0.974928i 0.0747301 + 0.997204i 0.543108 + 0.940691i 0.223308 0.386780i 0.900969 + 0.433884i 1.33425 + 1.23801i −0.826239 0.563320i
101.4 −0.623490 + 0.781831i 0.792429 2.01908i −0.222521 0.974928i 0.0747301 + 0.997204i 1.08451 + 1.87842i −2.30659 + 3.99514i 0.900969 + 0.433884i −1.24957 1.15943i −0.826239 0.563320i
111.1 0.900969 + 0.433884i −2.07183 1.41255i 0.623490 + 0.781831i −0.733052 + 0.680173i −1.25377 2.17160i −0.525199 + 0.909671i 0.222521 + 0.974928i 1.20117 + 3.06053i −0.955573 + 0.294755i
111.2 0.900969 + 0.433884i −0.889549 0.606484i 0.623490 + 0.781831i −0.733052 + 0.680173i −0.538312 0.932384i 2.53031 4.38263i 0.222521 + 0.974928i −0.672549 1.71363i −0.955573 + 0.294755i
111.3 0.900969 + 0.433884i 1.41868 + 0.967239i 0.623490 + 0.781831i −0.733052 + 0.680173i 0.858516 + 1.48699i −0.475578 + 0.823725i 0.222521 + 0.974928i −0.0189247 0.0482195i −0.955573 + 0.294755i
111.4 0.900969 + 0.433884i 2.49243 + 1.69931i 0.623490 + 0.781831i −0.733052 + 0.680173i 1.50830 + 2.61245i 0.376122 0.651463i 0.222521 + 0.974928i 2.22854 + 5.67822i −0.955573 + 0.294755i
181.1 −0.623490 0.781831i −3.32148 0.500633i −0.222521 + 0.974928i 0.826239 + 0.563320i 1.67950 + 2.90898i −0.871475 + 1.50944i 0.900969 0.433884i 7.91489 + 2.44142i −0.0747301 0.997204i
181.2 −0.623490 0.781831i −1.49662 0.225578i −0.222521 + 0.974928i 0.826239 + 0.563320i 0.756760 + 1.31075i 1.14635 1.98553i 0.900969 0.433884i −0.677747 0.209057i −0.0747301 0.997204i
181.3 −0.623490 0.781831i 0.118518 + 0.0178637i −0.222521 + 0.974928i 0.826239 + 0.563320i −0.0599282 0.103799i −1.86141 + 3.22406i 0.900969 0.433884i −2.85299 0.880031i −0.0747301 0.997204i
181.4 −0.623490 0.781831i 2.98823 + 0.450403i −0.222521 + 0.974928i 0.826239 + 0.563320i −1.51099 2.61711i −2.05024 + 3.55112i 0.900969 0.433884i 5.85992 + 1.80755i −0.0747301 0.997204i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 411.4
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.g even 21 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 430.2.q.c 48
43.g even 21 1 inner 430.2.q.c 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
430.2.q.c 48 1.a even 1 1 trivial
430.2.q.c 48 43.g even 21 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{3}^{48} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(430, [\chi])\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database