Properties

Label 390.2.t
Level $390$
Weight $2$
Character orbit 390.t
Rep. character $\chi_{390}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $28$
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.t (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(i)\)
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 184 28 156
Cusp forms 152 28 124
Eisenstein series 32 0 32

Trace form

\( 28 q - 28 q^{4} - 4 q^{5} + O(q^{10}) \) \( 28 q - 28 q^{4} - 4 q^{5} + 8 q^{11} + 12 q^{13} - 8 q^{15} + 28 q^{16} + 4 q^{17} + 4 q^{18} - 8 q^{19} + 4 q^{20} - 16 q^{21} - 16 q^{23} + 12 q^{25} + 24 q^{31} - 12 q^{34} - 48 q^{37} - 8 q^{39} + 12 q^{41} + 32 q^{43} - 8 q^{44} + 16 q^{46} + 48 q^{47} + 60 q^{49} + 16 q^{50} - 12 q^{52} - 60 q^{53} - 32 q^{55} - 40 q^{58} + 8 q^{59} + 8 q^{60} - 16 q^{61} - 28 q^{64} - 60 q^{65} - 16 q^{66} - 4 q^{68} - 16 q^{69} - 56 q^{70} - 16 q^{71} - 4 q^{72} + 8 q^{76} + 48 q^{77} + 16 q^{78} - 4 q^{80} - 28 q^{81} + 4 q^{82} + 48 q^{83} + 16 q^{84} - 28 q^{85} + 48 q^{87} + 12 q^{89} + 4 q^{90} + 48 q^{91} + 16 q^{92} - 48 q^{95} - 8 q^{99} + O(q^{100}) \)

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.t.a 390.t 65.f $12$ $3.114$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}-\beta _{7}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
390.2.t.b 390.t 65.f $16$ $3.114$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+\beta _{8}q^{3}-q^{4}-\beta _{10}q^{5}+\beta _{5}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(390, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)