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Properties

Label 448.2.b
Level $448$
Weight $2$
Character orbit 448.b
Rep. character $\chi_{448}(225,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $128$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(31\)

Dimensions

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

Total New Old
Modular forms 76 12 64
Cusp forms 52 12 40
Eisenstein series 24 0 24

Trace form

\( 12 q - 12 q^{9} + O(q^{10}) \) \( 12 q - 12 q^{9} + 24 q^{17} - 36 q^{25} - 48 q^{33} + 24 q^{41} + 12 q^{49} + 48 q^{57} + 24 q^{73} - 36 q^{81} + 24 q^{89} + 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
448.2.b.a 448.b 8.b $2$ $3.577$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{5}-q^{7}-q^{9}-iq^{11}+\cdots\)
448.2.b.b 448.b 8.b $2$ $3.577$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-iq^{11}+\cdots\)
448.2.b.c 448.b 8.b $4$ $3.577$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
448.2.b.d 448.b 8.b $4$ $3.577$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \)