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Properties

Label 448.6.m
Level $448$
Weight $6$
Character orbit 448.m
Rep. character $\chi_{448}(113,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 448.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(448, [\chi])\).

Total New Old
Modular forms 656 120 536
Cusp forms 624 120 504
Eisenstein series 32 0 32

Trace form

\( 120 q + O(q^{10}) \) \( 120 q - 604 q^{11} + 3600 q^{15} - 4720 q^{19} + 7464 q^{27} - 4072 q^{29} + 10648 q^{37} - 14724 q^{43} - 288120 q^{49} - 20880 q^{51} - 24728 q^{53} - 30504 q^{59} + 96160 q^{61} - 79380 q^{63} - 55376 q^{65} - 30580 q^{67} - 44640 q^{69} + 320984 q^{75} - 7448 q^{77} - 105720 q^{79} - 787320 q^{81} + 126440 q^{83} + 264800 q^{85} - 362352 q^{93} - 577600 q^{95} - 584140 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

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