Properties

Label 448.2.i
Level $448$
Weight $2$
Character orbit 448.i
Rep. character $\chi_{448}(65,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $28$
Newform subspaces $10$
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.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
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 36 116
Cusp forms 104 28 76
Eisenstein series 48 8 40

Trace form

\( 28q + 2q^{5} - 12q^{9} + O(q^{10}) \) \( 28q + 2q^{5} - 12q^{9} + 24q^{13} - 2q^{17} - 18q^{21} - 8q^{25} + 24q^{29} + 10q^{33} - 14q^{37} - 8q^{41} - 12q^{45} - 4q^{49} - 6q^{53} + 4q^{57} + 18q^{61} - 12q^{65} - 4q^{69} - 2q^{73} + 14q^{77} + 10q^{81} + 36q^{85} + 14q^{89} - 18q^{93} - 40q^{97} + O(q^{100}) \)

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.i.a \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(-1\) \(-4\) \(q+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
448.2.i.b \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(-4\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
448.2.i.c \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(4\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
448.2.i.d \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(4\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
448.2.i.e \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-4\) \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
448.2.i.f \(2\) \(3.577\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(-1\) \(4\) \(q+(3-3\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-2\zeta_{6})q^{7}+\cdots\)
448.2.i.g \(4\) \(3.577\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-2\) \(2\) \(4\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(2\beta _{1}-\beta _{2}+2\beta _{3})q^{5}+\cdots\)
448.2.i.h \(4\) \(3.577\) \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{1}q^{3}+3\beta _{2}q^{5}+\beta _{3}q^{7}+4\beta _{2}q^{9}+\cdots\)
448.2.i.i \(4\) \(3.577\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(1-\zeta_{12}^{2})q^{5}+\cdots\)
448.2.i.j \(4\) \(3.577\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(-4\) \(q+(1+\beta _{1}+\beta _{2})q^{3}+(-2\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)