Properties

Label 32.4.a
Level $32$
Weight $4$
Character orbit 32.a
Rep. character $\chi_{32}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $16$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 32 = 2^{5} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 32.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(16\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(32))\).

Total New Old
Modular forms 16 3 13
Cusp forms 8 3 5
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.
\(+\)\(2\)
\(-\)\(1\)

Trace form

\( 3q + 2q^{5} + 47q^{9} + O(q^{10}) \) \( 3q + 2q^{5} + 47q^{9} - 118q^{13} - 154q^{17} + 256q^{21} + 309q^{25} - 198q^{29} - 640q^{33} + 834q^{37} + 590q^{41} - 1334q^{45} - 517q^{49} - 302q^{53} + 640q^{57} + 890q^{61} + 604q^{65} + 768q^{69} - 162q^{73} - 1280q^{77} + 11q^{81} - 1468q^{85} - 2322q^{89} + 5120q^{93} + 374q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(32))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
32.4.a.a \(1\) \(1.888\) \(\Q\) None \(0\) \(-8\) \(-10\) \(-16\) \(-\) \(q-8q^{3}-10q^{5}-2^{4}q^{7}+37q^{9}+40q^{11}+\cdots\)
32.4.a.b \(1\) \(1.888\) \(\Q\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(22\) \(0\) \(+\) \(q+22q^{5}-3^{3}q^{9}-18q^{13}-94q^{17}+\cdots\)
32.4.a.c \(1\) \(1.888\) \(\Q\) None \(0\) \(8\) \(-10\) \(16\) \(+\) \(q+8q^{3}-10q^{5}+2^{4}q^{7}+37q^{9}-40q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(32))\) into lower level spaces

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