Properties

Label 160.4.a
Level $160$
Weight $4$
Character orbit 160.a
Rep. character $\chi_{160}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $7$
Sturm bound $96$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 160.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(160))\).

Total New Old
Modular forms 80 12 68
Cusp forms 64 12 52
Eisenstein series 16 0 16

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.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(5\)

Trace form

\( 12q + 68q^{9} + O(q^{10}) \) \( 12q + 68q^{9} + 144q^{13} + 152q^{17} - 376q^{21} + 300q^{25} + 56q^{29} + 1232q^{33} - 1008q^{37} - 176q^{41} + 440q^{45} + 1204q^{49} - 784q^{53} + 416q^{57} - 2560q^{61} + 280q^{65} - 1064q^{69} - 2088q^{73} - 944q^{77} - 1020q^{81} + 2648q^{89} - 3472q^{93} - 2488q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(160))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5
160.4.a.a \(1\) \(9.440\) \(\Q\) None \(0\) \(-2\) \(-5\) \(6\) \(+\) \(+\) \(q-2q^{3}-5q^{5}+6q^{7}-23q^{9}+60q^{11}+\cdots\)
160.4.a.b \(1\) \(9.440\) \(\Q\) None \(0\) \(2\) \(-5\) \(-6\) \(-\) \(+\) \(q+2q^{3}-5q^{5}-6q^{7}-23q^{9}-60q^{11}+\cdots\)
160.4.a.c \(2\) \(9.440\) \(\Q(\sqrt{6}) \) None \(0\) \(-8\) \(10\) \(-8\) \(+\) \(-\) \(q+(-4+\beta )q^{3}+5q^{5}+(-4-5\beta )q^{7}+\cdots\)
160.4.a.d \(2\) \(9.440\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-10\) \(0\) \(-\) \(+\) \(q-\beta q^{3}-5q^{5}+7\beta q^{7}-7q^{9}+2\beta q^{11}+\cdots\)
160.4.a.e \(2\) \(9.440\) \(\Q(\sqrt{13}) \) None \(0\) \(0\) \(-10\) \(0\) \(+\) \(+\) \(q-\beta q^{3}-5q^{5}-\beta q^{7}+5^{2}q^{9}-6\beta q^{11}+\cdots\)
160.4.a.f \(2\) \(9.440\) \(\Q(\sqrt{10}) \) None \(0\) \(0\) \(10\) \(0\) \(-\) \(-\) \(q+\beta q^{3}+5q^{5}+3\beta q^{7}+13q^{9}-2\beta q^{11}+\cdots\)
160.4.a.g \(2\) \(9.440\) \(\Q(\sqrt{6}) \) None \(0\) \(8\) \(10\) \(8\) \(-\) \(-\) \(q+(4+\beta )q^{3}+5q^{5}+(4-5\beta )q^{7}+(13+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(160))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(160)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 2}\)