Properties

Label 57.2.a
Level $57$
Weight $2$
Character orbit 57.a
Rep. character $\chi_{57}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $13$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 57 = 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 57.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(13\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(57))\).

Total New Old
Modular forms 8 3 5
Cusp forms 5 3 2
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(1\)
\(-\)\(+\)\(-\)\(2\)
Plus space\(+\)\(1\)
Minus space\(-\)\(2\)

Trace form

\( 3 q - 3 q^{2} + q^{3} + 3 q^{4} - 4 q^{5} + q^{6} - 2 q^{7} - 3 q^{8} + 3 q^{9} + 2 q^{10} - 2 q^{11} - q^{12} + 2 q^{13} + 4 q^{14} + 2 q^{15} - 9 q^{16} - 4 q^{17} - 3 q^{18} - 3 q^{19} - 2 q^{20}+ \cdots - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(57))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 19
57.2.a.a 57.a 1.a $1$ $0.455$ \(\Q\) None 57.2.a.a \(-2\) \(-1\) \(-3\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
57.2.a.b 57.a 1.a $1$ $0.455$ \(\Q\) None 57.2.a.b \(-2\) \(1\) \(1\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
57.2.a.c 57.a 1.a $1$ $0.455$ \(\Q\) None 57.2.a.c \(1\) \(1\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(57))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(57)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)