Properties

Label 156.4.i
Level $156$
Weight $4$
Character orbit 156.i
Rep. character $\chi_{156}(61,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $2$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 156.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(156, [\chi])\).

Total New Old
Modular forms 180 16 164
Cusp forms 156 16 140
Eisenstein series 24 0 24

Trace form

\( 16 q + 20 q^{5} + 4 q^{7} - 72 q^{9} + O(q^{10}) \) \( 16 q + 20 q^{5} + 4 q^{7} - 72 q^{9} + 8 q^{11} - 24 q^{13} - 12 q^{15} - 22 q^{17} - 64 q^{19} + 156 q^{21} + 216 q^{23} + 476 q^{25} + 150 q^{29} - 408 q^{31} + 96 q^{33} - 520 q^{35} + 290 q^{37} - 180 q^{39} - 886 q^{41} - 152 q^{43} - 90 q^{45} + 896 q^{47} - 42 q^{49} - 48 q^{51} + 2108 q^{53} - 480 q^{55} - 168 q^{57} + 1336 q^{59} - 2060 q^{61} + 36 q^{63} - 2146 q^{65} - 2616 q^{67} - 288 q^{69} - 272 q^{71} + 3416 q^{73} + 312 q^{75} + 1352 q^{77} + 3656 q^{79} - 648 q^{81} - 3360 q^{83} + 2666 q^{85} - 900 q^{87} + 1028 q^{89} - 5280 q^{91} - 1134 q^{93} - 1192 q^{95} + 234 q^{97} - 144 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(156, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
156.4.i.a 156.i 13.c $8$ $9.204$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-12\) \(14\) \(-11\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3-3\beta _{2})q^{3}+(2+\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
156.4.i.b 156.i 13.c $8$ $9.204$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(12\) \(6\) \(15\) $\mathrm{SU}(2)[C_{3}]$ \(q+3\beta _{1}q^{3}+(1+\beta _{4}+\beta _{5})q^{5}+(4-4\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(156, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)