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Properties

Label 105.5.l
Level $105$
Weight $5$
Character orbit 105.l
Rep. character $\chi_{105}(22,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $48$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(105, [\chi])\).

Total New Old
Modular forms 136 48 88
Cusp forms 120 48 72
Eisenstein series 16 0 16

Trace form

\( 48 q + 96 q^{5} - 72 q^{6} + O(q^{10}) \) \( 48 q + 96 q^{5} - 72 q^{6} - 80 q^{10} + 720 q^{12} + 680 q^{13} - 3128 q^{16} - 2640 q^{17} - 1128 q^{20} + 4120 q^{22} - 360 q^{23} + 1264 q^{25} + 3840 q^{26} + 4176 q^{30} + 2112 q^{31} - 4200 q^{32} - 1080 q^{33} + 8856 q^{36} + 2320 q^{37} - 4200 q^{38} - 9928 q^{40} - 5760 q^{41} + 12400 q^{43} + 3888 q^{45} - 5120 q^{46} - 5760 q^{47} - 11520 q^{48} - 14616 q^{50} - 8064 q^{51} - 2640 q^{52} - 14880 q^{53} + 3920 q^{55} + 21168 q^{56} + 7920 q^{57} + 8480 q^{58} + 16128 q^{60} - 8432 q^{61} - 8040 q^{62} + 19872 q^{65} - 2304 q^{66} + 14400 q^{67} + 42600 q^{68} + 6272 q^{70} + 14832 q^{71} - 20840 q^{73} - 9936 q^{75} - 66848 q^{76} - 11760 q^{77} + 16200 q^{78} - 30288 q^{80} - 34992 q^{81} + 50720 q^{82} + 32160 q^{83} - 13296 q^{85} + 50160 q^{86} - 11520 q^{87} - 78120 q^{88} + 3456 q^{90} - 15720 q^{92} - 6480 q^{93} - 2904 q^{95} + 8136 q^{96} - 42840 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.5.l.a 105.l 5.c $48$ $10.854$ None \(0\) \(0\) \(96\) \(0\) $\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{5}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)