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Properties

Label 448.2.m
Level $448$
Weight $2$
Character orbit 448.m
Rep. character $\chi_{448}(113,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $24$
Newform subspaces $4$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(128\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 144 24 120
Cusp forms 112 24 88
Eisenstein series 32 0 32

Trace form

\( 24 q + O(q^{10}) \) \( 24 q + 4 q^{11} + 16 q^{15} + 16 q^{19} - 24 q^{27} - 8 q^{29} - 8 q^{37} + 28 q^{43} - 24 q^{49} - 16 q^{51} + 8 q^{53} + 24 q^{59} + 32 q^{61} - 20 q^{63} - 16 q^{65} - 20 q^{67} + 32 q^{69} + 24 q^{75} + 8 q^{77} + 8 q^{79} - 24 q^{81} + 40 q^{83} - 32 q^{85} - 48 q^{93} - 64 q^{95} - 44 q^{99} + O(q^{100}) \)

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.m.a 448.m 16.e $2$ $3.577$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{5}+iq^{7}+3iq^{9}+(-1+\cdots)q^{11}+\cdots\)
448.2.m.b 448.m 16.e $2$ $3.577$ \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}+(-2-2i)q^{5}-iq^{7}+\cdots\)
448.2.m.c 448.m 16.e $8$ $3.577$ 8.0.214798336.3 None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}+\beta _{1}q^{5}+\beta _{5}q^{7}+(-\beta _{5}-\beta _{7})q^{9}+\cdots\)
448.2.m.d 448.m 16.e $12$ $3.577$ 12.0.\(\cdots\).1 None \(0\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5})q^{5}-\beta _{3}q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)