↑

Properties

Label 448.6.bc
Level $448$
Weight $6$
Character orbit 448.bc
Rep. character $\chi_{448}(29,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1920$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 448.bc (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 2576 1920 656
Cusp forms 2544 1920 624
Eisenstein series 32 0 32

Trace form

\( 1920 q + O(q^{10}) \) \( 1920 q - 13592 q^{22} + 51920 q^{26} - 64880 q^{30} - 74320 q^{32} - 25520 q^{34} + 62320 q^{36} + 124720 q^{40} - 65512 q^{44} - 83520 q^{51} - 466560 q^{54} + 440192 q^{55} - 150920 q^{56} - 51984 q^{58} + 197856 q^{60} + 351264 q^{62} - 317520 q^{63} - 122320 q^{67} + 14304 q^{68} - 286944 q^{70} - 828144 q^{72} - 377720 q^{74} + 772992 q^{75} - 536960 q^{76} - 1054992 q^{78} - 710720 q^{79} - 387200 q^{80} + 1443728 q^{86} + 446560 q^{88} - 1842544 q^{92} - 1642560 q^{94} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)