Properties

Label 32.6.a
Level $32$
Weight $6$
Character orbit 32.a
Rep. character $\chi_{32}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 32.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(32))\).

Total New Old
Modular forms 24 5 19
Cusp forms 16 5 11
Eisenstein series 8 0 8

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

\(2\)Dim.
\(+\)\(2\)
\(-\)\(3\)

Trace form

\( 5q + 38q^{5} + 449q^{9} + O(q^{10}) \) \( 5q + 38q^{5} + 449q^{9} + 110q^{13} + 1610q^{17} - 5888q^{21} - 4277q^{25} + 3678q^{29} + 13184q^{33} - 7258q^{37} - 30766q^{41} + 63214q^{45} + 57789q^{49} - 76490q^{53} - 132992q^{57} + 108510q^{61} + 113476q^{65} - 226560q^{69} - 120318q^{73} + 195328q^{77} + 270029q^{81} - 131124q^{85} - 174702q^{89} + 152576q^{93} + 359642q^{97} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(32))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
32.6.a.a \(1\) \(5.132\) \(\Q\) None \(0\) \(-8\) \(14\) \(-208\) \(+\) \(q-8q^{3}+14q^{5}-208q^{7}-179q^{9}+\cdots\)
32.6.a.b \(1\) \(5.132\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-82\) \(0\) \(+\) \(q-82q^{5}-3^{5}q^{9}-1194q^{13}+2242q^{17}+\cdots\)
32.6.a.c \(1\) \(5.132\) \(\Q\) None \(0\) \(8\) \(14\) \(208\) \(-\) \(q+8q^{3}+14q^{5}+208q^{7}-179q^{9}+\cdots\)
32.6.a.d \(2\) \(5.132\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(92\) \(0\) \(-\) \(q+\beta q^{3}+46q^{5}-6\beta q^{7}+525q^{9}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(32))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(32)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)