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Properties

Label 68.4.b
Level $68$
Weight $4$
Character orbit 68.b
Rep. character $\chi_{68}(33,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 68 = 2^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 68.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(68, [\chi])\).

Total New Old
Modular forms 30 4 26
Cusp forms 24 4 20
Eisenstein series 6 0 6

Trace form

\( 4 q - 60 q^{9} + O(q^{10}) \) \( 4 q - 60 q^{9} - 32 q^{13} + 32 q^{15} + 28 q^{17} + 160 q^{19} - 136 q^{21} + 164 q^{25} - 104 q^{33} - 304 q^{35} - 144 q^{43} + 1120 q^{47} + 932 q^{49} - 848 q^{51} + 24 q^{53} - 640 q^{55} - 336 q^{59} + 320 q^{67} - 2600 q^{69} - 744 q^{77} + 3292 q^{81} + 2224 q^{83} - 1488 q^{85} + 3520 q^{87} - 3136 q^{89} + 2584 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(68, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
68.4.b.a 68.b 17.b $4$ $4.012$ 4.0.1499912.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+(-15+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(68, [\chi])\) into lower level spaces

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