↑

Properties

Label 448.6.z
Level $448$
Weight $6$
Character orbit 448.z
Rep. character $\chi_{448}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $312$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 448.z (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 1312 328 984
Cusp forms 1248 312 936
Eisenstein series 64 16 48

Trace form

\( 312 q + 6 q^{3} - 6 q^{5} + 8 q^{7} + O(q^{10}) \) \( 312 q + 6 q^{3} - 6 q^{5} + 8 q^{7} + 606 q^{11} - 12 q^{17} + 6 q^{19} - 490 q^{21} + 1676 q^{23} - 8152 q^{29} - 12 q^{33} + 8642 q^{35} - 10650 q^{37} + 4 q^{39} - 32064 q^{43} + 1452 q^{45} - 8 q^{49} + 9154 q^{51} - 24730 q^{53} - 43434 q^{59} - 6 q^{61} - 4 q^{65} - 75206 q^{67} - 287664 q^{71} - 18744 q^{75} + 33610 q^{77} + 813560 q^{81} - 12508 q^{85} + 12 q^{87} + 197552 q^{91} + 970 q^{93} + 726416 q^{99} + O(q^{100}) \)

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

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