Properties

Label 572.2.b
Level $572$
Weight $2$
Character orbit 572.b
Rep. character $\chi_{572}(571,\cdot)$
Character field $\Q$
Dimension $80$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 572 \)
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 88 88 0
Cusp forms 80 80 0
Eisenstein series 8 8 0

Trace form

\( 80q - 4q^{4} - 80q^{9} + O(q^{10}) \) \( 80q - 4q^{4} - 80q^{9} - 4q^{14} + 12q^{16} - 16q^{22} - 72q^{25} + 4q^{26} + 14q^{36} + 14q^{38} + 38q^{42} - 14q^{48} - 80q^{49} - 16q^{53} + 6q^{56} - 4q^{64} + 34q^{66} - 16q^{69} + 44q^{77} - 22q^{78} + 64q^{81} - 60q^{82} + 76q^{88} - 18q^{92} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
572.2.b.a \(4\) \(4.567\) \(\Q(\sqrt{-2}, \sqrt{-13})\) \(\Q(\sqrt{-13}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}-2q^{4}+\beta _{2}q^{7}+2\beta _{2}q^{8}+\cdots\)
572.2.b.b \(20\) \(4.567\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) \(\Q(\sqrt{-143}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{2}-\beta _{9}q^{3}+\beta _{12}q^{4}+(-\beta _{3}+\cdots)q^{6}+\cdots\)
572.2.b.c \(56\) \(4.567\) None \(0\) \(0\) \(0\) \(0\)