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Properties

Label 448.4.bc
Level $448$
Weight $4$
Character orbit 448.bc
Rep. character $\chi_{448}(29,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $1152$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 448.bc (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 64 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(256\)

Dimensions

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

Total New Old
Modular forms 1552 1152 400
Cusp forms 1520 1152 368
Eisenstein series 32 0 32

Trace form

\( 1152 q + O(q^{10}) \) \( 1152 q - 472 q^{22} + 80 q^{26} + 2320 q^{30} + 2480 q^{32} + 2000 q^{34} + 880 q^{36} - 3280 q^{40} - 1000 q^{44} - 5952 q^{51} + 3456 q^{54} - 1152 q^{55} - 392 q^{56} - 4752 q^{58} - 4896 q^{60} - 5856 q^{62} + 5040 q^{63} + 4080 q^{67} - 4128 q^{68} - 2016 q^{70} + 1296 q^{72} + 2632 q^{74} - 8832 q^{75} + 11904 q^{76} - 10128 q^{78} - 11328 q^{79} - 18560 q^{80} + 1040 q^{86} + 6240 q^{88} + 25232 q^{92} + 17856 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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

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

\( S_{4}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 2}\)