Properties

Label 112.2.f
Level 112
Weight 2
Character orbit f
Rep. character \(\chi_{112}(111,\cdot)\)
Character field \(\Q\)
Dimension 4
Newforms 2
Sturm bound 32
Trace bound 3

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Defining parameters

Level: \( N \) = \( 112 = 2^{4} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 112.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).

Total New Old
Modular forms 22 4 18
Cusp forms 10 4 6
Eisenstein series 12 0 12

Trace form

\(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut -\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 24q^{29} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 24q^{53} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 48q^{65} \) \(\mathstrut -\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 44q^{81} \) \(\mathstrut -\mathstrut 64q^{93} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
112.2.f.a \(2\) \(0.894\) \(\Q(\sqrt{-3}) \) None \(0\) \(-4\) \(0\) \(4\) \(q-2q^{3}-2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots\)
112.2.f.b \(2\) \(0.894\) \(\Q(\sqrt{-3}) \) None \(0\) \(4\) \(0\) \(-4\) \(q+2q^{3}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(112, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)