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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
448.2.b.a \(2\) \(3.577\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-2\) \(q+iq^{3}-2iq^{5}-q^{7}-q^{9}-iq^{11}+\cdots\)
448.2.b.b \(2\) \(3.577\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(2\) \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}-iq^{11}+\cdots\)
448.2.b.c \(4\) \(3.577\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{12}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
448.2.b.d \(4\) \(3.577\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(4\) \(q-\zeta_{12}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)