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Properties

Label 104.4.o
Level $104$
Weight $4$
Character orbit 104.o
Rep. character $\chi_{104}(17,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $1$
Sturm bound $56$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 104 = 2^{3} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 104.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(56\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(104, [\chi])\).

Total New Old
Modular forms 92 20 72
Cusp forms 76 20 56
Eisenstein series 16 0 16

Trace form

\( 20 q - 6 q^{3} - 54 q^{7} - 72 q^{9} + O(q^{10}) \) \( 20 q - 6 q^{3} - 54 q^{7} - 72 q^{9} - 42 q^{11} + 24 q^{13} - 70 q^{17} - 102 q^{19} + 90 q^{23} - 628 q^{25} + 708 q^{27} + 170 q^{29} - 678 q^{33} - 544 q^{35} + 582 q^{37} + 1162 q^{39} + 438 q^{41} + 270 q^{43} + 540 q^{45} + 92 q^{49} - 444 q^{51} - 592 q^{53} - 288 q^{55} + 90 q^{59} + 746 q^{61} - 1068 q^{63} - 1412 q^{65} + 846 q^{67} + 682 q^{69} - 1038 q^{71} + 722 q^{75} + 2812 q^{77} - 1008 q^{79} + 694 q^{81} - 180 q^{85} - 338 q^{87} + 2466 q^{89} + 690 q^{91} - 4764 q^{93} - 2592 q^{95} - 846 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(104, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
104.4.o.a 104.o 13.e $20$ $6.136$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(-6\) \(0\) \(-54\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1}-\beta _{7}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(104, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(104, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)