Properties

Label 448.2.q
Level $448$
Weight $2$
Character orbit 448.q
Rep. character $\chi_{448}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $32$
Newform subspaces $3$
Sturm bound $128$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 152 32 120
Cusp forms 104 32 72
Eisenstein series 48 0 48

Trace form

\( 32q + 16q^{9} + O(q^{10}) \) \( 32q + 16q^{9} - 16q^{25} + 16q^{49} + 32q^{57} - 48q^{73} + 32q^{81} - 144q^{89} + O(q^{100}) \)

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.q.a \(8\) \(3.577\) 8.0.12960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{7})q^{3}+\beta _{6}q^{5}+(2\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
448.2.q.b \(12\) \(3.577\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) \(q-\beta _{5}q^{3}+(\beta _{6}-\beta _{7})q^{5}+(\beta _{4}-\beta _{10}+\cdots)q^{7}+\cdots\)
448.2.q.c \(12\) \(3.577\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) \(q-\beta _{5}q^{3}+(-\beta _{6}+\beta _{7})q^{5}+(-\beta _{4}+\beta _{10}+\cdots)q^{7}+\cdots\)

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

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