Properties

Label 105.3.t
Level $105$
Weight $3$
Character orbit 105.t
Rep. character $\chi_{105}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $2$
Sturm bound $48$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(105, [\chi])\).

Total New Old
Modular forms 72 44 28
Cusp forms 56 44 12
Eisenstein series 16 0 16

Trace form

\( 44 q + 48 q^{4} + 8 q^{6} - 2 q^{7} + 6 q^{9} + O(q^{10}) \) \( 44 q + 48 q^{4} + 8 q^{6} - 2 q^{7} + 6 q^{9} + 10 q^{12} - 92 q^{13} - 20 q^{15} - 96 q^{16} - 66 q^{18} + 86 q^{19} - 40 q^{21} + 184 q^{22} - 116 q^{24} + 110 q^{25} + 60 q^{27} + 36 q^{28} + 20 q^{30} - 58 q^{31} - 148 q^{33} - 368 q^{34} + 24 q^{36} - 38 q^{37} - 34 q^{39} + 126 q^{42} - 156 q^{43} + 60 q^{45} - 120 q^{46} + 860 q^{48} + 10 q^{49} + 44 q^{51} - 188 q^{52} - 204 q^{54} - 40 q^{55} - 100 q^{57} + 64 q^{58} - 150 q^{60} - 60 q^{61} - 202 q^{63} - 112 q^{64} - 128 q^{66} + 146 q^{67} - 24 q^{69} + 60 q^{70} + 26 q^{72} + 98 q^{73} + 912 q^{76} - 608 q^{78} - 10 q^{79} + 158 q^{81} - 248 q^{82} + 444 q^{84} + 120 q^{85} + 482 q^{87} + 216 q^{88} + 180 q^{90} + 102 q^{91} + 162 q^{93} + 272 q^{94} + 412 q^{96} + 1168 q^{97} + 312 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.3.t.a 105.t 21.h $8$ $2.861$ 8.0.3317760000.8 None \(0\) \(-4\) \(0\) \(56\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{2}-\beta _{4}-\beta _{5})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{3}+\cdots\)
105.3.t.b 105.t 21.h $36$ $2.861$ None \(0\) \(4\) \(0\) \(-58\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)