Properties

Label 136.4.b
Level $136$
Weight $4$
Character orbit 136.b
Rep. character $\chi_{136}(33,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 136 = 2^{3} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 136.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(136, [\chi])\).

Total New Old
Modular forms 58 14 44
Cusp forms 50 14 36
Eisenstein series 8 0 8

Trace form

\( 14 q - 174 q^{9} + O(q^{10}) \) \( 14 q - 174 q^{9} - 28 q^{13} - 98 q^{17} + 24 q^{19} + 104 q^{21} - 634 q^{25} + 584 q^{33} - 656 q^{35} + 200 q^{43} + 240 q^{47} - 1142 q^{49} + 864 q^{51} + 1396 q^{53} + 960 q^{55} + 1608 q^{59} - 936 q^{67} + 312 q^{69} - 8 q^{77} + 1542 q^{81} + 3768 q^{83} - 816 q^{85} - 6208 q^{87} + 92 q^{89} - 3208 q^{93} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(136, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
136.4.b.a $6$ $8.024$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
136.4.b.b $8$ $8.024$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-\beta _{4}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(136, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(136, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)