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Properties

Label 448.4.bn
Level $448$
Weight $4$
Character orbit 448.bn
Rep. character $\chi_{448}(37,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $3040$
Sturm bound $256$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 448.bn (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 448 \)
Character field: \(\Q(\zeta_{48})\)
Sturm bound: \(256\)

Dimensions

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

Total New Old
Modular forms 3104 3104 0
Cusp forms 3040 3040 0
Eisenstein series 64 64 0

Trace form

\( 3040 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9} + O(q^{10}) \) \( 3040 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 32 q^{13} - 16 q^{14} - 32 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 32 q^{20} - 16 q^{21} + 912 q^{22} - 8 q^{23} - 2008 q^{24} - 8 q^{25} - 8 q^{26} - 32 q^{27} + 744 q^{28} - 32 q^{29} + 2312 q^{30} - 8 q^{32} - 32 q^{34} - 16 q^{35} - 1792 q^{36} - 8 q^{37} - 888 q^{38} - 8 q^{39} - 8 q^{40} - 32 q^{41} - 3176 q^{42} - 32 q^{43} - 1008 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 32 q^{48} - 16 q^{49} + 5680 q^{50} - 8 q^{51} - 3320 q^{52} - 8 q^{53} - 8 q^{54} - 32 q^{55} - 16 q^{56} - 32 q^{57} - 8 q^{58} - 2760 q^{59} - 4904 q^{60} - 8 q^{61} - 160 q^{62} - 32 q^{63} - 12128 q^{64} - 16 q^{65} + 5336 q^{66} + 4072 q^{67} - 8 q^{68} - 32 q^{69} - 16 q^{70} + 864 q^{71} - 8 q^{72} - 8 q^{73} + 2624 q^{74} - 8 q^{75} - 32 q^{76} - 16 q^{77} + 14080 q^{78} - 8 q^{79} - 5024 q^{80} - 8 q^{81} + 6952 q^{82} - 32 q^{83} - 4160 q^{84} - 32 q^{85} - 8 q^{86} - 8 q^{87} - 8 q^{88} - 8 q^{89} + 18688 q^{90} - 16 q^{91} - 32 q^{92} - 440 q^{93} - 8 q^{94} - 12928 q^{96} + 12088 q^{98} - 464 q^{99} + O(q^{100}) \)

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.