Properties

Label 2800.1.f
Level $2800$
Weight $1$
Character orbit 2800.f
Rep. character $\chi_{2800}(2001,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $480$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2800.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(480\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(2800, [\chi])\).

Total New Old
Modular forms 56 7 49
Cusp forms 20 4 16
Eisenstein series 36 3 33

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 0

Trace form

\( 4 q + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{9} + 4 q^{11} - 2 q^{21} + 2 q^{39} - 2 q^{51} - 2 q^{71} + 2 q^{91} + 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(2800, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2800.1.f.a 2800.f 7.b $1$ $1.397$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{9}+q^{11}+q^{23}-q^{29}-q^{37}+\cdots\)
2800.1.f.b 2800.f 7.b $1$ $1.397$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{9}+q^{11}-q^{23}-q^{29}+q^{37}+\cdots\)
2800.1.f.c 2800.f 7.b $2$ $1.397$ \(\Q(\sqrt{-1}) \) $D_{3}$ \(\Q(\sqrt{-35}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}+iq^{7}+q^{11}-iq^{13}+iq^{17}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(2800, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(2800, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 5}\)