Newspace parameters
| Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
| Weight: | \( k \) | \(=\) | \( 2 \) |
| Character orbit: | \([\chi]\) | \(=\) | 175.a (trivial) |
Newform invariants
| Self dual: | yes |
| Analytic conductor: | \(1.39738203537\) |
| Analytic rank: | \(1\) |
| Dimension: | \(1\) |
| Coefficient field: | \(\mathbb{Q}\) |
| Coefficient ring: | \(\mathbb{Z}\) |
| Coefficient ring index: | \( 1 \) |
| Twist minimal: | no (minimal twist has level 35) |
| 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 |
|
−2.00000 | −1.00000 | 2.00000 | 0 | 2.00000 | 1.00000 | 0 | −2.00000 | 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 | 175.2.a.a | 1 | |
| 3.b | odd | 2 | 1 | 1575.2.a.k | 1 | ||
| 4.b | odd | 2 | 1 | 2800.2.a.w | 1 | ||
| 5.b | even | 2 | 1 | 175.2.a.c | 1 | ||
| 5.c | odd | 4 | 2 | 35.2.b.a | ✓ | 2 | |
| 7.b | odd | 2 | 1 | 1225.2.a.a | 1 | ||
| 15.d | odd | 2 | 1 | 1575.2.a.a | 1 | ||
| 15.e | even | 4 | 2 | 315.2.d.a | 2 | ||
| 20.d | odd | 2 | 1 | 2800.2.a.l | 1 | ||
| 20.e | even | 4 | 2 | 560.2.g.b | 2 | ||
| 35.c | odd | 2 | 1 | 1225.2.a.i | 1 | ||
| 35.f | even | 4 | 2 | 245.2.b.a | 2 | ||
| 35.k | even | 12 | 4 | 245.2.j.d | 4 | ||
| 35.l | odd | 12 | 4 | 245.2.j.e | 4 | ||
| 40.i | odd | 4 | 2 | 2240.2.g.h | 2 | ||
| 40.k | even | 4 | 2 | 2240.2.g.g | 2 | ||
| 60.l | odd | 4 | 2 | 5040.2.t.p | 2 | ||
| 105.k | odd | 4 | 2 | 2205.2.d.b | 2 | ||
| By twisted newform orbit | |||||||
|---|---|---|---|---|---|---|---|
| Twist | Min | Dim | Char | Parity | Ord | Mult | Type |
| 35.2.b.a | ✓ | 2 | 5.c | odd | 4 | 2 | |
| 175.2.a.a | 1 | 1.a | even | 1 | 1 | trivial | |
| 175.2.a.c | 1 | 5.b | even | 2 | 1 | ||
| 245.2.b.a | 2 | 35.f | even | 4 | 2 | ||
| 245.2.j.d | 4 | 35.k | even | 12 | 4 | ||
| 245.2.j.e | 4 | 35.l | odd | 12 | 4 | ||
| 315.2.d.a | 2 | 15.e | even | 4 | 2 | ||
| 560.2.g.b | 2 | 20.e | even | 4 | 2 | ||
| 1225.2.a.a | 1 | 7.b | odd | 2 | 1 | ||
| 1225.2.a.i | 1 | 35.c | odd | 2 | 1 | ||
| 1575.2.a.a | 1 | 15.d | odd | 2 | 1 | ||
| 1575.2.a.k | 1 | 3.b | odd | 2 | 1 | ||
| 2205.2.d.b | 2 | 105.k | odd | 4 | 2 | ||
| 2240.2.g.g | 2 | 40.k | even | 4 | 2 | ||
| 2240.2.g.h | 2 | 40.i | odd | 4 | 2 | ||
| 2800.2.a.l | 1 | 20.d | odd | 2 | 1 | ||
| 2800.2.a.w | 1 | 4.b | odd | 2 | 1 | ||
| 5040.2.t.p | 2 | 60.l | odd | 4 | 2 | ||
Hecke kernels
This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(175))\).
Hecke characteristic polynomials
| $p$ | $F_p(T)$ |
|---|---|
| $2$ | \( 2 + T \) |
| $3$ | \( 1 + T \) |
| $5$ | \( T \) |
| $7$ | \( -1 + T \) |
| $11$ | \( 3 + T \) |
| $13$ | \( 1 + T \) |
| $17$ | \( 7 + T \) |
| $19$ | \( T \) |
| $23$ | \( 6 + T \) |
| $29$ | \( 5 + T \) |
| $31$ | \( -2 + T \) |
| $37$ | \( 2 + T \) |
| $41$ | \( -2 + T \) |
| $43$ | \( -4 + T \) |
| $47$ | \( -3 + T \) |
| $53$ | \( 6 + T \) |
| $59$ | \( -10 + T \) |
| $61$ | \( 8 + T \) |
| $67$ | \( 2 + T \) |
| $71$ | \( 8 + T \) |
| $73$ | \( 6 + T \) |
| $79$ | \( 5 + T \) |
| $83$ | \( -4 + T \) |
| $89$ | \( T \) |
| $97$ | \( 7 + T \) |
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