↑

Properties

Label 3822.2.dm
Level $3822$
Weight $2$
Character orbit 3822.dm
Rep. character $\chi_{3822}(121,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1560$
Sturm bound $1568$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.dm (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1568\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3822, [\chi])\).

Total New Old
Modular forms 9504 1560 7944
Cusp forms 9312 1560 7752
Eisenstein series 192 0 192

Trace form

\( 1560 q - 4 q^{3} - 130 q^{4} - 2 q^{7} - 260 q^{9} + O(q^{10}) \) \( 1560 q - 4 q^{3} - 130 q^{4} - 2 q^{7} - 260 q^{9} + 16 q^{10} - 2 q^{12} + 2 q^{13} - 8 q^{14} + 130 q^{16} - 4 q^{17} + 14 q^{21} + 4 q^{22} - 126 q^{25} - 32 q^{26} - 4 q^{27} - 4 q^{28} + 4 q^{29} + 36 q^{35} - 130 q^{36} + 82 q^{37} + 52 q^{38} + 52 q^{39} + 8 q^{40} + 36 q^{41} + 10 q^{43} - 12 q^{44} + 180 q^{47} - 12 q^{48} - 58 q^{49} + 104 q^{51} - 2 q^{52} + 4 q^{53} + 164 q^{55} - 32 q^{56} - 74 q^{61} - 32 q^{62} + 12 q^{63} + 260 q^{64} + 28 q^{65} + 16 q^{66} + 4 q^{68} - 24 q^{69} + 48 q^{70} + 36 q^{71} - 210 q^{73} + 52 q^{74} - 6 q^{75} + 6 q^{76} + 152 q^{77} - 64 q^{78} + 32 q^{79} - 260 q^{81} + 48 q^{82} + 16 q^{84} + 144 q^{85} + 216 q^{86} - 12 q^{87} - 20 q^{88} + 24 q^{89} + 16 q^{90} + 28 q^{91} + 24 q^{93} - 108 q^{94} + 112 q^{95} - 150 q^{97} + 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3822, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3822, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3822, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1274, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1911, [\chi])\)\(^{\oplus 2}\)