Newspace parameters
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(0.0474111762001\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{2}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{4}\) |
Projective field: | Galois closure of 4.2.475.1 |
Artin image: | $D_8$ |
Artin field: | Galois closure of 8.2.4286875.1 |
$q$-expansion
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{2}\). We also show the integral \(q\)-expansion of the trace form.
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | ||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
94.1 |
|
−1.41421 | 1.41421 | 1.00000 | −1.00000 | −2.00000 | 0 | 0 | 1.00000 | 1.41421 | ||||||||||||||||||||||||
94.2 | 1.41421 | −1.41421 | 1.00000 | −1.00000 | −2.00000 | 0 | 0 | 1.00000 | −1.41421 | |||||||||||||||||||||||||
Inner twists
Char | Parity | Ord | Mult | Type |
---|---|---|---|---|
1.a | even | 1 | 1 | trivial |
95.d | odd | 2 | 1 | CM by \(\Q(\sqrt{-95}) \) |
5.b | even | 2 | 1 | inner |
19.b | odd | 2 | 1 | inner |
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 95.1.d.b | ✓ | 2 |
3.b | odd | 2 | 1 | 855.1.g.c | 2 | ||
4.b | odd | 2 | 1 | 1520.1.m.b | 2 | ||
5.b | even | 2 | 1 | inner | 95.1.d.b | ✓ | 2 |
5.c | odd | 4 | 2 | 475.1.c.b | 2 | ||
15.d | odd | 2 | 1 | 855.1.g.c | 2 | ||
19.b | odd | 2 | 1 | inner | 95.1.d.b | ✓ | 2 |
19.c | even | 3 | 2 | 1805.1.h.b | 4 | ||
19.d | odd | 6 | 2 | 1805.1.h.b | 4 | ||
19.e | even | 9 | 6 | 1805.1.o.b | 12 | ||
19.f | odd | 18 | 6 | 1805.1.o.b | 12 | ||
20.d | odd | 2 | 1 | 1520.1.m.b | 2 | ||
57.d | even | 2 | 1 | 855.1.g.c | 2 | ||
76.d | even | 2 | 1 | 1520.1.m.b | 2 | ||
95.d | odd | 2 | 1 | CM | 95.1.d.b | ✓ | 2 |
95.g | even | 4 | 2 | 475.1.c.b | 2 | ||
95.h | odd | 6 | 2 | 1805.1.h.b | 4 | ||
95.i | even | 6 | 2 | 1805.1.h.b | 4 | ||
95.o | odd | 18 | 6 | 1805.1.o.b | 12 | ||
95.p | even | 18 | 6 | 1805.1.o.b | 12 | ||
285.b | even | 2 | 1 | 855.1.g.c | 2 | ||
380.d | even | 2 | 1 | 1520.1.m.b | 2 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
95.1.d.b | ✓ | 2 | 1.a | even | 1 | 1 | trivial |
95.1.d.b | ✓ | 2 | 5.b | even | 2 | 1 | inner |
95.1.d.b | ✓ | 2 | 19.b | odd | 2 | 1 | inner |
95.1.d.b | ✓ | 2 | 95.d | odd | 2 | 1 | CM |
475.1.c.b | 2 | 5.c | odd | 4 | 2 | ||
475.1.c.b | 2 | 95.g | even | 4 | 2 | ||
855.1.g.c | 2 | 3.b | odd | 2 | 1 | ||
855.1.g.c | 2 | 15.d | odd | 2 | 1 | ||
855.1.g.c | 2 | 57.d | even | 2 | 1 | ||
855.1.g.c | 2 | 285.b | even | 2 | 1 | ||
1520.1.m.b | 2 | 4.b | odd | 2 | 1 | ||
1520.1.m.b | 2 | 20.d | odd | 2 | 1 | ||
1520.1.m.b | 2 | 76.d | even | 2 | 1 | ||
1520.1.m.b | 2 | 380.d | even | 2 | 1 | ||
1805.1.h.b | 4 | 19.c | even | 3 | 2 | ||
1805.1.h.b | 4 | 19.d | odd | 6 | 2 | ||
1805.1.h.b | 4 | 95.h | odd | 6 | 2 | ||
1805.1.h.b | 4 | 95.i | even | 6 | 2 | ||
1805.1.o.b | 12 | 19.e | even | 9 | 6 | ||
1805.1.o.b | 12 | 19.f | odd | 18 | 6 | ||
1805.1.o.b | 12 | 95.o | odd | 18 | 6 | ||
1805.1.o.b | 12 | 95.p | even | 18 | 6 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2}^{2} - 2 \)
acting on \(S_{1}^{\mathrm{new}}(95, [\chi])\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T^{2} - 2 \)
$3$
\( T^{2} - 2 \)
$5$
\( (T + 1)^{2} \)
$7$
\( T^{2} \)
$11$
\( T^{2} \)
$13$
\( T^{2} - 2 \)
$17$
\( T^{2} \)
$19$
\( (T + 1)^{2} \)
$23$
\( T^{2} \)
$29$
\( T^{2} \)
$31$
\( T^{2} \)
$37$
\( T^{2} - 2 \)
$41$
\( T^{2} \)
$43$
\( T^{2} \)
$47$
\( T^{2} \)
$53$
\( T^{2} - 2 \)
$59$
\( T^{2} \)
$61$
\( T^{2} \)
$67$
\( T^{2} - 2 \)
$71$
\( T^{2} \)
$73$
\( T^{2} \)
$79$
\( T^{2} \)
$83$
\( T^{2} \)
$89$
\( T^{2} \)
$97$
\( T^{2} - 2 \)
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