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Properties

Label 567.1.d
Level $567$
Weight $1$
Character orbit 567.d
Rep. character $\chi_{567}(244,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $72$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 567.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(72\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(567, [\chi])\).

Total New Old
Modular forms 19 8 11
Cusp forms 7 4 3
Eisenstein series 12 4 8

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

\( 4 q + 4 q^{4} + O(q^{10}) \) \( 4 q + 4 q^{4} - 4 q^{22} + 4 q^{25} - 4 q^{28} - 4 q^{46} + 4 q^{49} - 4 q^{58} - 4 q^{67} - 4 q^{79} - 8 q^{88} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field Image CM RM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
567.1.d.a 567.d 7.b $1$ $0.283$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None 567.1.d.a \(-1\) \(0\) \(0\) \(1\) \(q-q^{2}+q^{7}+q^{8}-q^{11}-q^{14}-q^{16}+\cdots\)
567.1.d.b 567.d 7.b $1$ $0.283$ \(\Q\) $D_{3}$ \(\Q(\sqrt{-7}) \) None 567.1.d.a \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{7}-q^{8}+q^{11}+q^{14}-q^{16}+\cdots\)
567.1.d.c 567.d 7.b $2$ $0.283$ \(\Q(\sqrt{3}) \) $D_{6}$ \(\Q(\sqrt{-7}) \) None 567.1.d.c \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{2}+2q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(567, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)