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Properties

Label 390.2.be
Level $390$
Weight $2$
Character orbit 390.be
Rep. character $\chi_{390}(17,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $112$
Newform subspaces $2$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 2 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(390, [\chi])\).

Total New Old
Modular forms 368 112 256
Cusp forms 304 112 192
Eisenstein series 64 0 64

Trace form

\( 112 q + O(q^{10}) \) \( 112 q + 24 q^{13} + 56 q^{16} + 24 q^{27} - 12 q^{30} - 36 q^{33} - 8 q^{36} + 24 q^{37} + 16 q^{40} + 12 q^{42} + 8 q^{43} - 60 q^{45} - 24 q^{46} - 48 q^{51} - 24 q^{52} + 8 q^{55} - 24 q^{58} + 48 q^{61} - 168 q^{63} - 32 q^{66} - 24 q^{67} - 24 q^{72} + 24 q^{75} - 48 q^{76} - 36 q^{78} - 56 q^{81} + 48 q^{82} - 96 q^{85} + 72 q^{87} - 24 q^{90} - 36 q^{93} + 72 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(390, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
390.2.be.a 390.be 195.af $16$ $3.114$ 16.0.\(\cdots\).1 None \(0\) \(-4\) \(0\) \(-24\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{11}-\beta _{12})q^{3}+\beta _{2}q^{4}+\cdots\)
390.2.be.b 390.be 195.af $96$ $3.114$ None \(0\) \(4\) \(0\) \(24\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(390, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)