Properties

Label 160.2.a
Level $160$
Weight $2$
Character orbit 160.a
Rep. character $\chi_{160}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 160.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(160))\).

Total New Old
Modular forms 32 4 28
Cusp forms 17 4 13
Eisenstein series 15 0 15

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

\(2\)\(5\)FrickeDim.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4q + 12q^{9} + O(q^{10}) \) \( 4q + 12q^{9} - 16q^{13} + 8q^{17} - 8q^{21} + 4q^{25} + 8q^{29} - 16q^{33} - 16q^{37} - 16q^{41} + 8q^{45} - 4q^{49} + 16q^{53} - 32q^{57} + 8q^{65} + 40q^{69} + 8q^{73} + 48q^{77} - 20q^{81} + 8q^{89} + 16q^{93} + 24q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(160))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
160.2.a.a \(1\) \(1.278\) \(\Q\) None \(0\) \(-2\) \(-1\) \(-2\) \(+\) \(+\) \(q-2q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}+\cdots\)
160.2.a.b \(1\) \(1.278\) \(\Q\) None \(0\) \(2\) \(-1\) \(2\) \(-\) \(+\) \(q+2q^{3}-q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
160.2.a.c \(2\) \(1.278\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(+\) \(-\) \(q+\beta q^{3}+q^{5}-\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(160)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)