Properties

Label 448.2.p
Level $448$
Weight $2$
Character orbit 448.p
Rep. character $\chi_{448}(255,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $28$
Newform subspaces $5$
Sturm bound $128$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(128\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 152 36 116
Cusp forms 104 28 76
Eisenstein series 48 8 40

Trace form

\( 28q + 6q^{5} - 12q^{9} + O(q^{10}) \) \( 28q + 6q^{5} - 12q^{9} - 6q^{17} + 14q^{21} + 4q^{25} - 8q^{29} - 6q^{33} + 18q^{37} - 12q^{45} - 4q^{49} - 6q^{53} + 4q^{57} + 6q^{61} + 8q^{65} - 6q^{73} - 6q^{77} - 22q^{81} + 76q^{85} - 54q^{89} - 18q^{93} + O(q^{100}) \)

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.p.a \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-4\) \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
448.2.p.b \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(4\) \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
448.2.p.c \(4\) \(3.577\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
448.2.p.d \(4\) \(3.577\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(6\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1+\zeta_{12}^{2})q^{5}+\cdots\)
448.2.p.e \(16\) \(3.577\) 16.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{14}q^{3}+\beta _{13}q^{5}+\beta _{9}q^{7}+(-\beta _{3}+\cdots)q^{9}+\cdots\)

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

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