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Properties

Label 105.2.s
Level $105$
Weight $2$
Character orbit 105.s
Rep. character $\chi_{105}(26,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $4$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 40 20 20
Cusp forms 24 20 4
Eisenstein series 16 0 16

Trace form

\( 20 q + 8 q^{4} - 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 20 q + 8 q^{4} - 6 q^{7} - 4 q^{9} - 30 q^{12} + 4 q^{15} + 12 q^{16} - 2 q^{18} - 6 q^{19} + 6 q^{21} - 56 q^{22} + 18 q^{24} - 10 q^{25} + 4 q^{28} + 2 q^{30} - 54 q^{31} + 24 q^{33} + 12 q^{36} + 6 q^{37} + 6 q^{39} + 30 q^{42} + 36 q^{43} - 18 q^{45} - 20 q^{46} + 14 q^{49} - 12 q^{51} + 48 q^{52} + 24 q^{54} + 36 q^{57} - 32 q^{58} - 6 q^{60} + 12 q^{61} - 34 q^{63} + 72 q^{64} - 12 q^{66} + 34 q^{67} - 10 q^{72} + 42 q^{73} - 48 q^{78} - 26 q^{79} - 4 q^{81} + 72 q^{82} - 48 q^{84} - 24 q^{85} - 6 q^{87} - 16 q^{88} + 6 q^{91} + 42 q^{93} - 48 q^{94} - 18 q^{96} - 104 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.2.s.a 105.s 21.g $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+(1+\cdots)q^{4}+\cdots\)
105.2.s.b 105.s 21.g $2$ $0.838$ \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
105.2.s.c 105.s 21.g $8$ $0.838$ 8.0.856615824.2 None \(-3\) \(1\) \(4\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{3})q^{2}+(1-\beta _{1}+\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
105.2.s.d 105.s 21.g $8$ $0.838$ 8.0.856615824.2 None \(3\) \(2\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(1+\beta _{3}+\beta _{6})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

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