↑

Properties

Label 399.2.bc
Level $399$
Weight $2$
Character orbit 399.bc
Rep. character $\chi_{399}(248,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $1$
Sturm bound $106$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 399 = 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 399.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(106\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(399, [\chi])\).

Total New Old
Modular forms 116 96 20
Cusp forms 100 96 4
Eisenstein series 16 0 16

Trace form

\( 96 q + 48 q^{4} - 4 q^{7} - 8 q^{9} + O(q^{10}) \) \( 96 q + 48 q^{4} - 4 q^{7} - 8 q^{9} - 12 q^{10} - 30 q^{12} + 8 q^{15} - 32 q^{16} - 2 q^{18} + 8 q^{21} - 48 q^{22} + 36 q^{24} - 60 q^{25} - 8 q^{28} - 28 q^{30} + 12 q^{31} - 6 q^{33} - 16 q^{36} - 16 q^{39} + 24 q^{40} - 12 q^{42} - 36 q^{45} - 12 q^{46} + 4 q^{49} + 18 q^{51} + 36 q^{52} - 36 q^{54} - 12 q^{58} + 8 q^{60} - 72 q^{61} + 8 q^{63} - 8 q^{64} + 48 q^{66} + 8 q^{67} + 64 q^{70} + 16 q^{72} + 24 q^{73} + 30 q^{75} + 12 q^{78} - 44 q^{79} - 36 q^{82} - 84 q^{84} - 56 q^{85} + 24 q^{87} - 4 q^{88} + 36 q^{91} + 48 q^{93} - 36 q^{94} + 168 q^{96} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(399, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
399.2.bc.a 399.bc 21.g $96$ $3.186$ None 399.2.bc.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(399, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(399, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)