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Properties

Label 572.2.f
Level $572$
Weight $2$
Character orbit 572.f
Rep. character $\chi_{572}(441,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $3$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(572, [\chi])\).

Total New Old
Modular forms 90 14 76
Cusp forms 78 14 64
Eisenstein series 12 0 12

Trace form

\( 14 q + 22 q^{9} + O(q^{10}) \) \( 14 q + 22 q^{9} - 6 q^{13} + 8 q^{23} - 22 q^{25} - 12 q^{27} - 4 q^{29} - 8 q^{35} + 20 q^{39} + 12 q^{43} - 18 q^{49} - 8 q^{51} + 32 q^{53} - 16 q^{61} + 36 q^{65} - 28 q^{69} + 20 q^{75} - 8 q^{77} - 8 q^{79} + 30 q^{81} + 20 q^{87} - 12 q^{91} - 12 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(572, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
572.2.f.a 572.f 13.b $2$ $4.567$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4iq^{7}-3q^{9}-iq^{11}+(-3+2i)q^{13}+\cdots\)
572.2.f.b 572.f 13.b $4$ $4.567$ \(\Q(i, \sqrt{21})\) None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{3}+(\beta _{1}-\beta _{2})q^{7}+(3-\beta _{3})q^{9}+\cdots\)
572.2.f.c 572.f 13.b $8$ $4.567$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(\beta _{1}+\beta _{5}+\beta _{6}-\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(572, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(572, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)