Properties

Label 448.2.f
Level 448
Weight 2
Character orbit f
Rep. character \(\chi_{448}(447,\cdot)\)
Character field \(\Q\)
Dimension 14
Newforms 4
Sturm bound 128
Trace bound 3

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Defining parameters

Level: \( N \) = \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 448.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 28 \)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(448, [\chi])\).

Total New Old
Modular forms 76 18 58
Cusp forms 52 14 38
Eisenstein series 24 4 20

Trace form

\( 14q + 6q^{9} + O(q^{10}) \) \( 14q + 6q^{9} + 16q^{21} - 10q^{25} - 4q^{29} + 12q^{37} - 2q^{49} + 12q^{53} - 16q^{57} + 16q^{65} + 12q^{77} - 50q^{81} - 64q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(448, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
448.2.f.a \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(-4\) \(0\) \(-4\) \(q-2q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\)
448.2.f.b \(2\) \(3.577\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{7}-3q^{9}-2\beta q^{11}-2\beta q^{23}+\cdots\)
448.2.f.c \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(4\) \(0\) \(4\) \(q+2q^{3}+2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots\)
448.2.f.d \(8\) \(3.577\) \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{2}q^{3}-\zeta_{16}^{5}q^{5}-\zeta_{16}^{4}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)