Properties

Label 390.2.bn
Level $390$
Weight $2$
Character orbit 390.bn
Rep. character $\chi_{390}(67,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $3$
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.bn (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 3 \)
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 56 312
Cusp forms 304 56 248
Eisenstein series 64 0 64

Trace form

\( 56 q - 4 q^{2} - 28 q^{4} + 8 q^{8} + O(q^{10}) \) \( 56 q - 4 q^{2} - 28 q^{4} + 8 q^{8} - 8 q^{11} + 16 q^{13} - 8 q^{15} - 28 q^{16} + 4 q^{17} + 40 q^{19} + 16 q^{21} - 16 q^{23} - 36 q^{25} + 24 q^{31} - 4 q^{32} + 8 q^{33} - 36 q^{34} + 12 q^{37} - 8 q^{39} - 12 q^{41} + 8 q^{43} - 8 q^{44} + 8 q^{45} + 8 q^{46} + 36 q^{49} - 40 q^{50} - 8 q^{52} + 12 q^{53} + 56 q^{55} - 24 q^{56} - 48 q^{58} + 8 q^{59} - 8 q^{60} - 32 q^{61} - 72 q^{62} + 56 q^{64} - 92 q^{65} + 16 q^{66} - 72 q^{67} - 8 q^{68} - 16 q^{69} - 48 q^{70} - 32 q^{71} - 24 q^{73} + 60 q^{74} - 32 q^{76} + 48 q^{77} + 16 q^{78} + 28 q^{81} + 40 q^{82} + 16 q^{84} + 100 q^{85} + 48 q^{87} - 36 q^{89} + 4 q^{90} - 48 q^{91} + 32 q^{92} + 24 q^{94} + 48 q^{95} + 4 q^{98} - 8 q^{99} + O(q^{100}) \)

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.bn.a 390.bn 65.o $8$ $3.114$ \(\Q(\zeta_{24})\) None \(4\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{4}q^{2}+\zeta_{24}q^{3}+(-1+\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
390.2.bn.b 390.bn 65.o $16$ $3.114$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(8\) \(0\) \(0\) \(24\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\beta _{14})q^{2}-\beta _{15}q^{3}+\beta _{14}q^{4}+\cdots\)
390.2.bn.c 390.bn 65.o $32$ $3.114$ None \(-16\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{12}]$

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

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