Properties

Label 156.2.w
Level $156$
Weight $2$
Character orbit 156.w
Rep. character $\chi_{156}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $4$
Sturm bound $56$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 156.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 4 \)
Sturm bound: \(56\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(156, [\chi])\).

Total New Old
Modular forms 128 56 72
Cusp forms 96 56 40
Eisenstein series 32 0 32

Trace form

\( 56 q - 4 q^{5} + 28 q^{9} + O(q^{10}) \) \( 56 q - 4 q^{5} + 28 q^{9} - 32 q^{14} - 8 q^{16} - 52 q^{20} + 8 q^{21} - 12 q^{22} + 12 q^{24} - 40 q^{26} - 28 q^{28} - 80 q^{32} - 24 q^{34} - 12 q^{37} + 56 q^{40} - 56 q^{41} + 12 q^{42} + 56 q^{44} - 8 q^{45} + 36 q^{46} + 16 q^{48} - 72 q^{49} + 52 q^{50} + 16 q^{52} - 24 q^{53} + 108 q^{56} - 48 q^{57} + 56 q^{58} + 16 q^{60} - 20 q^{61} + 60 q^{62} - 24 q^{65} + 16 q^{66} - 24 q^{68} - 16 q^{70} - 76 q^{73} + 24 q^{74} - 12 q^{76} + 4 q^{78} - 4 q^{80} - 28 q^{81} - 60 q^{82} + 4 q^{85} - 12 q^{88} + 100 q^{89} + 120 q^{92} - 8 q^{93} + 28 q^{94} - 40 q^{96} + 36 q^{97} + 148 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(156, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
156.2.w.a 156.w 52.l $4$ $1.246$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
156.2.w.b 156.w 52.l $4$ $1.246$ \(\Q(\zeta_{12})\) None \(4\) \(0\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
156.2.w.c 156.w 52.l $24$ $1.246$ None \(-4\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
156.2.w.d 156.w 52.l $24$ $1.246$ None \(-2\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)