Newspace parameters
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(10.3253342510\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
$q$-expansion
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 | \(\iota_m(\nu)\) | \( a_{2} \) | \( a_{3} \) | \( a_{4} \) | \( a_{5} \) | \( a_{6} \) | \( a_{7} \) | \( a_{8} \) | \( a_{9} \) | \( a_{10} \) | |||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1.1 |
|
1.00000 | 2.00000 | −7.00000 | 0 | 2.00000 | 7.00000 | −15.0000 | −23.0000 | 0 | |||||||||||||||||||||
Atkin-Lehner signs
\( p \) | Sign |
---|---|
\(5\) | \(1\) |
\(7\) | \(-1\) |
Inner twists
This newform does not admit any (nontrivial) inner twists.
Twists
By twisting character orbit | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Mult | Type | Twist | Min | Dim |
1.a | even | 1 | 1 | trivial | 175.4.a.b | 1 | |
3.b | odd | 2 | 1 | 1575.4.a.e | 1 | ||
5.b | even | 2 | 1 | 7.4.a.a | ✓ | 1 | |
5.c | odd | 4 | 2 | 175.4.b.b | 2 | ||
7.b | odd | 2 | 1 | 1225.4.a.j | 1 | ||
15.d | odd | 2 | 1 | 63.4.a.b | 1 | ||
20.d | odd | 2 | 1 | 112.4.a.f | 1 | ||
35.c | odd | 2 | 1 | 49.4.a.b | 1 | ||
35.i | odd | 6 | 2 | 49.4.c.b | 2 | ||
35.j | even | 6 | 2 | 49.4.c.c | 2 | ||
40.e | odd | 2 | 1 | 448.4.a.e | 1 | ||
40.f | even | 2 | 1 | 448.4.a.i | 1 | ||
55.d | odd | 2 | 1 | 847.4.a.b | 1 | ||
60.h | even | 2 | 1 | 1008.4.a.c | 1 | ||
65.d | even | 2 | 1 | 1183.4.a.b | 1 | ||
85.c | even | 2 | 1 | 2023.4.a.a | 1 | ||
105.g | even | 2 | 1 | 441.4.a.i | 1 | ||
105.o | odd | 6 | 2 | 441.4.e.h | 2 | ||
105.p | even | 6 | 2 | 441.4.e.e | 2 | ||
140.c | even | 2 | 1 | 784.4.a.g | 1 |
By twisted newform orbit | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
7.4.a.a | ✓ | 1 | 5.b | even | 2 | 1 | |
49.4.a.b | 1 | 35.c | odd | 2 | 1 | ||
49.4.c.b | 2 | 35.i | odd | 6 | 2 | ||
49.4.c.c | 2 | 35.j | even | 6 | 2 | ||
63.4.a.b | 1 | 15.d | odd | 2 | 1 | ||
112.4.a.f | 1 | 20.d | odd | 2 | 1 | ||
175.4.a.b | 1 | 1.a | even | 1 | 1 | trivial | |
175.4.b.b | 2 | 5.c | odd | 4 | 2 | ||
441.4.a.i | 1 | 105.g | even | 2 | 1 | ||
441.4.e.e | 2 | 105.p | even | 6 | 2 | ||
441.4.e.h | 2 | 105.o | odd | 6 | 2 | ||
448.4.a.e | 1 | 40.e | odd | 2 | 1 | ||
448.4.a.i | 1 | 40.f | even | 2 | 1 | ||
784.4.a.g | 1 | 140.c | even | 2 | 1 | ||
847.4.a.b | 1 | 55.d | odd | 2 | 1 | ||
1008.4.a.c | 1 | 60.h | even | 2 | 1 | ||
1183.4.a.b | 1 | 65.d | even | 2 | 1 | ||
1225.4.a.j | 1 | 7.b | odd | 2 | 1 | ||
1575.4.a.e | 1 | 3.b | odd | 2 | 1 | ||
2023.4.a.a | 1 | 85.c | even | 2 | 1 |
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator
\( T_{2} - 1 \)
acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(175))\).
Hecke characteristic polynomials
$p$
$F_p(T)$
$2$
\( T - 1 \)
$3$
\( T - 2 \)
$5$
\( T \)
$7$
\( T - 7 \)
$11$
\( T + 8 \)
$13$
\( T + 28 \)
$17$
\( T + 54 \)
$19$
\( T + 110 \)
$23$
\( T + 48 \)
$29$
\( T + 110 \)
$31$
\( T - 12 \)
$37$
\( T - 246 \)
$41$
\( T - 182 \)
$43$
\( T + 128 \)
$47$
\( T + 324 \)
$53$
\( T - 162 \)
$59$
\( T - 810 \)
$61$
\( T + 488 \)
$67$
\( T + 244 \)
$71$
\( T + 768 \)
$73$
\( T - 702 \)
$79$
\( T - 440 \)
$83$
\( T - 1302 \)
$89$
\( T - 730 \)
$97$
\( T + 294 \)
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