Properties

Label 448.2.f
Level $448$
Weight $2$
Character orbit 448.f
Rep. character $\chi_{448}(447,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $4$
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: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
448.2.f.a 448.f 28.d $2$ $3.577$ \(\Q(\sqrt{-3}) \) None 112.2.f.a \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-2 q^{3}-2\beta q^{5}+(-\beta-2)q^{7}+q^{9}+\cdots\)
448.2.f.b 448.f 28.d $2$ $3.577$ \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) 28.2.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{7}-3q^{9}-2\beta q^{11}-2\beta q^{23}+\cdots\)
448.2.f.c 448.f 28.d $2$ $3.577$ \(\Q(\sqrt{-3}) \) None 112.2.f.a \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2 q^{3}+2\beta q^{5}+(-\beta+2)q^{7}+q^{9}+\cdots\)
448.2.f.d 448.f 28.d $8$ $3.577$ \(\Q(\zeta_{16})\) None 224.2.f.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{2} q^{3}-\beta_{5} q^{5}-\beta_{4} q^{7}+(\beta_{7}+1)q^{9}+\cdots\)

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

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