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Properties

Label 2280.1.t
Level $2280$
Weight $1$
Character orbit 2280.t
Rep. character $\chi_{2280}(1139,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $10$
Sturm bound $480$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2280.t (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2280 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(480\)
Trace bound: \(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2280, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20 q - 4 q^{4} + 4 q^{6} - 4 q^{9} + 4 q^{16} + 4 q^{19} + 4 q^{24} + 12 q^{25} - 8 q^{30} + 12 q^{36} - 20 q^{49} + 4 q^{54} - 4 q^{64} - 8 q^{66} - 4 q^{76} + 4 q^{81} - 4 q^{96} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(2280, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2280.1.t.a 2280.t 2280.t $1$ $1.138$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) 2280.1.t.a \(-1\) \(-1\) \(-1\) \(0\) \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
2280.1.t.b 2280.t 2280.t $1$ $1.138$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) 2280.1.t.a \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
2280.1.t.c 2280.t 2280.t $1$ $1.138$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) 2280.1.t.a \(1\) \(-1\) \(1\) \(0\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
2280.1.t.d 2280.t 2280.t $1$ $1.138$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-570}) \) \(\Q(\sqrt{6}) \) 2280.1.t.a \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
2280.1.t.e 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{30}) \) 2280.1.t.e \(0\) \(0\) \(-2\) \(0\) \(q-i q^{2}-i q^{3}-q^{4}-q^{5}-q^{6}+\cdots\)
2280.1.t.f 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{190}) \) 2280.1.t.f \(0\) \(0\) \(0\) \(0\) \(q-i q^{2}+i q^{3}-q^{4}-i q^{5}+q^{6}+\cdots\)
2280.1.t.g 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{190}) \) 2280.1.t.f \(0\) \(0\) \(0\) \(0\) \(q+i q^{2}-i q^{3}-q^{4}-i q^{5}+q^{6}+\cdots\)
2280.1.t.h 2280.t 2280.t $2$ $1.138$ \(\Q(\sqrt{-1}) \) $D_{2}$ \(\Q(\sqrt{-95}) \), \(\Q(\sqrt{-114}) \) \(\Q(\sqrt{30}) \) 2280.1.t.e \(0\) \(0\) \(2\) \(0\) \(q-i q^{2}-i q^{3}-q^{4}+q^{5}-q^{6}+\cdots\)
2280.1.t.i 2280.t 2280.t $4$ $1.138$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-95}) \) None 2280.1.t.i \(0\) \(0\) \(-4\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}-q^{5}+\cdots\)
2280.1.t.j 2280.t 2280.t $4$ $1.138$ \(\Q(\zeta_{8})\) $D_{4}$ \(\Q(\sqrt{-95}) \) None 2280.1.t.i \(0\) \(0\) \(4\) \(0\) \(q+\zeta_{8}q^{2}-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+q^{5}-\zeta_{8}^{2}q^{6}+\cdots\)