Newform orbit 23.25.b.a

• Label: 23.25.b.a
• Level: $23$
• Weight: $25$
• Character orbit: 23.b
• Self dual: yes
• Analytic conductor: $83.942$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -23
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$23$
Weight:	$k$	$=$	$25$
Character orbit:	$[\chi]$	$=$	23.b (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$83.9424450193$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

$f(q)$

$=$

q - 1951 * q^2 - 1062686 * q^3 - 12970815 * q^4 + 2073300386 * q^6 + 58038408481 * q^8 + 846871998115 * q^9 + 13783903509090 * q^12 + 25363320370274 * q^13 + 104381230004609 * q^16 - 1652247268322365 * q^18 + 21914624432020321 * q^23 - 61676604155039966 * q^24 + 59604644775390625 * q^25 - 49483838042404574 * q^26 - 599825101783988924 * q^27 - 647932355939762206 * q^29 + 1237087799571624194 * q^31 - 1177370695120961055 * q^32 - 10984620016230013725 * q^36 - 26953245471004995964 * q^39 + 12576527614080568514 * q^41 - 42755432266871646271 * q^46 + 192261621286365409154 * q^47 - 110924471788677919774 * q^48 + 191581231380566414401 * q^49 - 116288661956787109375 * q^50 - 328982936308555553310 * q^52 + 1170258773580562390724 * q^54 + 1264116026438476063906 * q^58 - 3163397976515704019038 * q^59 - 2413558296964238802494 * q^62 + 545823784047988829761 * q^64 - 23288364579165946842206 * q^69 + 2861536906024780963394 * q^71 + 49151102957719032013315 * q^72 + 3932686548449574639554 * q^73 - 63341021537780761718750 * q^75 + 52585781913930747125764 * q^78 + 398244072228062297956549 * q^81 - 24536805375071189170814 * q^82 + 688548643604202139645316 * q^87 - 284250539302215659931615 * q^92 - 1314635885375571028225084 * q^93 - 375102423129698913259454 * q^94 + 1251175354515313619693730 * q^96 - 373774982423485074496351 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

22.1

0

−1951.00

−1.06269e6

−1.29708e7

0

2.07330e9

0

5.80384e10

8.46872e11

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
23.b	odd	2	1	CM by $\Q(\sqrt{-23})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	23.25.b.a	✓	1
23.b	odd	2	1	CM	23.25.b.a	✓	1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.25.b.a	✓	1	1.a	even	1	1	trivial
23.25.b.a	✓	1	23.b	odd	2	1	CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2} + 1951$ acting on $S_{25}^{\mathrm{new}}(23, [\chi])$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1951$
$3$	$T + 1062686$
$5$	$T$
$7$	$T$
$11$	$T$