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Properties

Label 104.4.i
Level $104$
Weight $4$
Character orbit 104.i
Rep. character $\chi_{104}(9,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $22$
Newform subspaces $3$
Sturm bound $56$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 92 22 70
Cusp forms 76 22 54
Eisenstein series 16 0 16

Trace form

\( 22 q + 6 q^{3} + 14 q^{5} + 18 q^{7} - 117 q^{9} + O(q^{10}) \) \( 22 q + 6 q^{3} + 14 q^{5} + 18 q^{7} - 117 q^{9} + 14 q^{11} - 9 q^{13} - 88 q^{15} - 113 q^{17} - 214 q^{19} + 20 q^{21} - 14 q^{23} + 812 q^{25} - 156 q^{27} + 35 q^{29} - 16 q^{31} - 22 q^{33} + 296 q^{35} - 553 q^{37} + 718 q^{39} + 475 q^{41} + 582 q^{43} - 87 q^{45} - 664 q^{47} - 713 q^{49} - 2244 q^{51} + 14 q^{53} - 648 q^{55} + 612 q^{57} + 578 q^{59} + 139 q^{61} + 1032 q^{63} - 515 q^{65} - 798 q^{67} - 1726 q^{69} + 906 q^{71} + 2742 q^{73} + 2798 q^{75} + 1620 q^{77} + 2520 q^{79} - 1627 q^{81} + 1248 q^{83} - 21 q^{85} - 278 q^{87} + 604 q^{89} - 4866 q^{91} - 200 q^{93} + 760 q^{95} - 1692 q^{97} - 5008 q^{99} + O(q^{100}) \)

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.i.a 104.i 13.c $2$ $6.136$ \(\Q(\sqrt{-3}) \) None \(0\) \(-8\) \(-18\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-8+8\zeta_{6})q^{3}-9q^{5}+4\zeta_{6}q^{7}+\cdots\)
104.4.i.b 104.i 13.c $8$ $6.136$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(11\) \(14\) \(15\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-\beta _{1}-3\beta _{2})q^{3}+(2-\beta _{4})q^{5}+(4\beta _{2}+\cdots)q^{7}+\cdots\)
104.4.i.c 104.i 13.c $12$ $6.136$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(18\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(2+\beta _{3}+\cdots)q^{5}+\cdots\)

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

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