↑

Properties

Label 156.4.b
Level $156$
Weight $4$
Character orbit 156.b
Rep. character $\chi_{156}(25,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $112$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 156.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 90 6 84
Cusp forms 78 6 72
Eisenstein series 12 0 12

Trace form

\( 6 q - 6 q^{3} + 54 q^{9} + O(q^{10}) \) \( 6 q - 6 q^{3} + 54 q^{9} - 34 q^{13} - 92 q^{17} + 136 q^{23} + 166 q^{25} - 54 q^{27} + 116 q^{29} - 56 q^{35} - 54 q^{39} - 632 q^{43} + 1042 q^{49} + 492 q^{51} - 1572 q^{53} + 960 q^{55} - 628 q^{61} - 536 q^{65} - 120 q^{69} + 426 q^{75} + 1776 q^{77} - 1568 q^{79} + 486 q^{81} - 276 q^{87} - 1736 q^{91} - 4968 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
156.4.b.a 156.b 13.b $2$ $9.204$ \(\Q(\sqrt{-3}) \) None 156.4.b.a \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3q^{3}+2\zeta_{6}q^{5}+3\zeta_{6}q^{7}+9q^{9}+\cdots\)
156.4.b.b 156.b 13.b $4$ $9.204$ 4.0.47664588.1 None 156.4.b.b \(0\) \(-12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+9q^{9}+(-3\beta _{1}+\cdots)q^{11}+\cdots\)

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

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