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Properties

Label 390.2.s
Level $390$
Weight $2$
Character orbit 390.s
Rep. character $\chi_{390}(77,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $56$
Newform subspaces $3$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.s (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 195 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

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

Total New Old
Modular forms 184 56 128
Cusp forms 152 56 96
Eisenstein series 32 0 32

Trace form

\( 56 q + O(q^{10}) \) \( 56 q - 56 q^{16} + 12 q^{27} + 12 q^{30} - 16 q^{36} - 16 q^{40} - 12 q^{42} + 16 q^{43} + 16 q^{55} - 48 q^{61} - 16 q^{66} - 84 q^{75} + 32 q^{81} + 96 q^{82} - 72 q^{87} - 12 q^{90} + 48 q^{91} + O(q^{100}) \)

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.s.a 390.s 195.s $8$ $3.114$ 8.0.40960000.1 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
390.2.s.b 390.s 195.s $24$ $3.114$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
390.2.s.c 390.s 195.s $24$ $3.114$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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