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Properties

Label 3762.2.l
Level $3762$
Weight $2$
Character orbit 3762.l
Rep. character $\chi_{3762}(463,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $400$
Sturm bound $1440$

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Defining parameters

Level: \( N \) \(=\) \( 3762 = 2 \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3762.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1440\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3762, [\chi])\).

Total New Old
Modular forms 1456 400 1056
Cusp forms 1424 400 1024
Eisenstein series 32 0 32

Trace form

\( 400 q - 200 q^{4} - 4 q^{7} + O(q^{10}) \) \( 400 q - 200 q^{4} - 4 q^{7} - 4 q^{13} - 32 q^{14} + 16 q^{15} - 200 q^{16} + 12 q^{17} + 16 q^{18} - 8 q^{19} + 24 q^{21} + 8 q^{23} + 400 q^{25} - 12 q^{27} - 4 q^{28} - 8 q^{30} - 4 q^{31} - 24 q^{35} + 8 q^{37} + 36 q^{39} + 64 q^{41} + 12 q^{42} - 4 q^{43} + 48 q^{45} + 104 q^{47} - 204 q^{49} + 8 q^{50} - 100 q^{51} - 4 q^{52} + 40 q^{53} + 36 q^{54} + 16 q^{56} + 44 q^{57} + 16 q^{59} + 4 q^{60} + 56 q^{61} + 12 q^{62} - 12 q^{63} + 400 q^{64} + 88 q^{65} - 28 q^{67} + 12 q^{68} + 20 q^{69} - 20 q^{71} + 16 q^{72} - 28 q^{73} - 12 q^{74} - 32 q^{75} + 4 q^{76} - 20 q^{78} - 4 q^{79} + 48 q^{81} - 16 q^{83} + 24 q^{84} + 40 q^{86} + 36 q^{87} + 60 q^{89} - 116 q^{90} + 52 q^{91} + 8 q^{92} + 24 q^{93} + 76 q^{95} + 8 q^{97} + 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3762, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3762, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3762, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1881, [\chi])\)\(^{\oplus 2}\)