Properties

Label 55.4.a
Level $55$
Weight $4$
Character orbit 55.a
Rep. character $\chi_{55}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $4$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 55.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(55))\).

Total New Old
Modular forms 20 10 10
Cusp forms 16 10 6
Eisenstein series 4 0 4

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

\(5\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(3\)

Trace form

\( 10 q + 52 q^{4} + 10 q^{5} + 56 q^{6} - 40 q^{7} - 12 q^{8} + 62 q^{9} - 60 q^{10} + 16 q^{12} + 8 q^{13} + 64 q^{14} + 60 q^{15} + 152 q^{16} + 64 q^{17} - 512 q^{18} - 312 q^{19} + 100 q^{20} - 232 q^{21}+ \cdots + 4920 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(55))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11
55.4.a.a 55.a 1.a $1$ $3.245$ \(\Q\) None 55.4.a.a \(1\) \(-3\) \(-5\) \(-9\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}-7q^{4}-5q^{5}-3q^{6}+\cdots\)
55.4.a.b 55.a 1.a $2$ $3.245$ \(\Q(\sqrt{17}) \) None 55.4.a.b \(-7\) \(-3\) \(10\) \(-25\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta )q^{2}+(-1-\beta )q^{3}+(5+7\beta )q^{4}+\cdots\)
55.4.a.c 55.a 1.a $3$ $3.245$ 3.3.568.1 None 55.4.a.c \(5\) \(-3\) \(-15\) \(-15\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}-\beta _{2})q^{2}+(-2-3\beta _{2})q^{3}+\cdots\)
55.4.a.d 55.a 1.a $4$ $3.245$ 4.4.1539480.1 None 55.4.a.d \(1\) \(9\) \(20\) \(9\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2-\beta _{2})q^{3}+(5+\beta _{1}+\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(55))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(55)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)