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Properties

Label 3920.2.dn
Level $3920$
Weight $2$
Character orbit 3920.dn
Rep. character $\chi_{3920}(449,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $996$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3920.dn (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 245 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3920, [\chi])\).

Total New Old
Modular forms 4104 1020 3084
Cusp forms 3960 996 2964
Eisenstein series 144 24 120

Trace form

\( 996 q - 5 q^{5} + 152 q^{9} + O(q^{10}) \) \( 996 q - 5 q^{5} + 152 q^{9} + 10 q^{11} + 11 q^{15} - 48 q^{19} - 22 q^{21} + 3 q^{25} - 30 q^{29} - 48 q^{31} - q^{35} + 22 q^{39} - 18 q^{41} - q^{45} - 16 q^{49} + 22 q^{51} - 17 q^{55} + 62 q^{59} - 10 q^{61} - 15 q^{65} - 14 q^{69} + 50 q^{71} + 101 q^{75} - 24 q^{79} - 192 q^{81} - 15 q^{85} - 10 q^{89} + 42 q^{91} - 18 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3920, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(245, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(490, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(980, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1960, [\chi])\)\(^{\oplus 2}\)