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Properties

Label 567.2.c
Level $567$
Weight $2$
Character orbit 567.c
Rep. character $\chi_{567}(566,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $3$
Sturm bound $144$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(567, [\chi])\).

Total New Old
Modular forms 84 36 48
Cusp forms 60 28 32
Eisenstein series 24 8 16

Trace form

\( 28 q - 20 q^{4} + O(q^{10}) \) \( 28 q - 20 q^{4} + 24 q^{16} + 32 q^{22} + 16 q^{25} + 8 q^{28} - 12 q^{37} - 36 q^{43} - 52 q^{46} + 4 q^{49} + 32 q^{58} - 24 q^{64} + 8 q^{67} + 24 q^{70} - 52 q^{79} + 36 q^{85} - 80 q^{88} - 60 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(567, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
567.2.c.a 567.c 21.c $8$ $4.528$ 8.0.\(\cdots\).3 \(\Q(\sqrt{-7}) \) 567.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+\beta _{4}q^{7}+(-2\beta _{1}+\cdots)q^{8}+\cdots\)
567.2.c.b 567.c 21.c $8$ $4.528$ 8.0.\(\cdots\).6 None 567.2.c.b \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{3}-\beta _{5})q^{2}-\beta _{1}q^{4}+\beta _{2}q^{5}+\cdots\)
567.2.c.c 567.c 21.c $12$ $4.528$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 63.2.o.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-\beta _{4}q^{4}-\beta _{3}q^{5}+(\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(567, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(567, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)