Properties

Label 128.2.a
Level 128
Weight 2
Character orbit a
Rep. character \(\chi_{128}(1,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 4
Sturm bound 32
Trace bound 5

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Defining parameters

Level: \( N \) = \( 128 = 2^{7} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 128.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(128))\).

Total New Old
Modular forms 24 4 20
Cusp forms 9 4 5
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.

\(2\)Dim.
\(+\)\(1\)
\(-\)\(3\)

Trace form

\(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 4q^{25} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut -\mathstrut 24q^{41} \) \(\mathstrut +\mathstrut 36q^{49} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 16q^{65} \) \(\mathstrut +\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 44q^{81} \) \(\mathstrut -\mathstrut 8q^{89} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(128))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2
128.2.a.a \(1\) \(1.022\) \(\Q\) None \(0\) \(-2\) \(-2\) \(-4\) \(+\) \(q-2q^{3}-2q^{5}-4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.b \(1\) \(1.022\) \(\Q\) None \(0\) \(-2\) \(2\) \(4\) \(-\) \(q-2q^{3}+2q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
128.2.a.c \(1\) \(1.022\) \(\Q\) None \(0\) \(2\) \(-2\) \(4\) \(-\) \(q+2q^{3}-2q^{5}+4q^{7}+q^{9}-2q^{11}+\cdots\)
128.2.a.d \(1\) \(1.022\) \(\Q\) None \(0\) \(2\) \(2\) \(-4\) \(-\) \(q+2q^{3}+2q^{5}-4q^{7}+q^{9}-2q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(128))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(128)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)