Properties

Label 105.3.c
Level $105$
Weight $3$
Character orbit 105.c
Rep. character $\chi_{105}(71,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $1$
Sturm bound $48$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 36 16 20
Cusp forms 28 16 12
Eisenstein series 8 0 8

Trace form

\( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{3} - 28 q^{4} - 28 q^{6} + 22 q^{9} - 20 q^{10} + 12 q^{12} + 10 q^{15} + 92 q^{16} - 52 q^{18} - 16 q^{19} - 14 q^{21} + 16 q^{22} + 128 q^{24} - 80 q^{25} - 148 q^{27} + 112 q^{28} + 80 q^{30} - 72 q^{31} - 4 q^{33} - 176 q^{34} - 76 q^{36} - 40 q^{37} + 90 q^{39} - 60 q^{40} + 280 q^{43} + 40 q^{45} + 72 q^{46} - 172 q^{48} + 112 q^{49} + 38 q^{51} - 88 q^{52} + 208 q^{54} + 80 q^{55} - 36 q^{57} - 24 q^{58} - 80 q^{60} - 56 q^{61} - 56 q^{63} - 44 q^{64} - 260 q^{66} - 120 q^{67} + 60 q^{69} + 376 q^{72} - 208 q^{73} - 40 q^{75} + 144 q^{76} - 228 q^{78} - 204 q^{79} + 458 q^{81} - 384 q^{82} - 84 q^{84} + 100 q^{85} - 324 q^{87} + 168 q^{88} - 160 q^{90} - 28 q^{91} + 108 q^{93} + 984 q^{94} + 40 q^{96} + 728 q^{97} - 166 q^{99} + O(q^{100}) \)

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.c.a 105.c 3.b $16$ $2.861$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}+(-2+\beta _{7}-\beta _{8}+\cdots)q^{4}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)