Properties

Label 156.3.d
Level $156$
Weight $3$
Character orbit 156.d
Rep. character $\chi_{156}(53,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 156.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(156, [\chi])\).

Total New Old
Modular forms 62 8 54
Cusp forms 50 8 42
Eisenstein series 12 0 12

Trace form

\( 8 q + 6 q^{3} - 8 q^{7} - 22 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{3} - 8 q^{7} - 22 q^{9} + 4 q^{15} - 24 q^{19} + 16 q^{21} - 28 q^{25} + 36 q^{27} + 96 q^{31} + 4 q^{33} - 96 q^{37} + 76 q^{43} - 136 q^{45} + 204 q^{49} - 62 q^{51} - 80 q^{55} + 184 q^{57} - 104 q^{61} + 36 q^{63} - 384 q^{67} - 8 q^{73} - 100 q^{75} + 328 q^{79} + 50 q^{81} - 64 q^{85} - 204 q^{87} - 52 q^{91} + 72 q^{93} + 416 q^{97} + 284 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(156, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
156.3.d.a 156.d 3.b $8$ $4.251$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(6\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)