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Properties

Label 448.4.m
Level $448$
Weight $4$
Character orbit 448.m
Rep. character $\chi_{448}(113,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $72$
Newform subspaces $2$
Sturm bound $256$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 448.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(448, [\chi])\).

Total New Old
Modular forms 400 72 328
Cusp forms 368 72 296
Eisenstein series 32 0 32

Trace form

\( 72 q + O(q^{10}) \) \( 72 q + 20 q^{11} - 240 q^{15} - 48 q^{19} + 264 q^{27} + 200 q^{29} + 8 q^{37} - 1268 q^{43} - 3528 q^{49} - 1488 q^{51} + 376 q^{53} + 2040 q^{59} - 1824 q^{61} + 1260 q^{63} + 976 q^{65} + 1020 q^{67} - 1056 q^{69} - 5512 q^{75} + 952 q^{77} - 8824 q^{79} - 5832 q^{81} - 2680 q^{83} - 480 q^{85} + 4272 q^{93} + 6080 q^{95} + 6212 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
448.4.m.a 448.m 16.e $34$ $26.433$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
448.4.m.b 448.m 16.e $38$ $26.433$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{4}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

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