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Properties

Label 53.2.b
Level $53$
Weight $2$
Character orbit 53.b
Rep. character $\chi_{53}(52,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $9$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 53.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 53 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(9\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(53, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 4 4 0
Eisenstein series 2 2 0

Trace form

\( 4 q - 4 q^{4} + 4 q^{6} - 8 q^{7} - 8 q^{9} + O(q^{10}) \) \( 4 q - 4 q^{4} + 4 q^{6} - 8 q^{7} - 8 q^{9} + 8 q^{10} + 4 q^{13} + 16 q^{15} - 12 q^{16} - 12 q^{17} + 20 q^{24} - 4 q^{25} - 12 q^{29} - 16 q^{36} + 28 q^{37} + 36 q^{38} - 16 q^{40} - 24 q^{42} - 8 q^{43} + 24 q^{44} - 12 q^{46} + 24 q^{47} - 4 q^{49} - 20 q^{52} - 12 q^{53} - 44 q^{54} - 12 q^{57} - 8 q^{60} - 24 q^{62} + 40 q^{63} + 4 q^{64} + 48 q^{66} + 12 q^{68} + 4 q^{69} + 8 q^{70} - 24 q^{77} - 28 q^{78} + 28 q^{81} + 24 q^{82} + 24 q^{89} + 56 q^{90} + 8 q^{91} - 48 q^{93} - 24 q^{95} + 28 q^{96} + 28 q^{97} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(53, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
53.2.b.a 53.b 53.b $4$ $0.423$ 4.0.7168.1 None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)