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Properties

Label 105.2.a
Level $105$
Weight $2$
Character orbit 105.a
Rep. character $\chi_{105}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $2$
Sturm bound $32$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(105))\).

Total New Old
Modular forms 20 3 17
Cusp forms 13 3 10
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(7\)FrickeDim
\(+\)\(+\)\(-\)$-$\(2\)
\(-\)\(-\)\(-\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(3\)

Trace form

\( 3 q + q^{2} - q^{3} + 5 q^{4} - q^{5} + q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + O(q^{10}) \) \( 3 q + q^{2} - q^{3} + 5 q^{4} - q^{5} + q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + q^{10} + 4 q^{11} - 7 q^{12} - 6 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 2 q^{17} + q^{18} - 4 q^{19} - 7 q^{20} - q^{21} - 20 q^{22} + 16 q^{23} - 3 q^{24} + 3 q^{25} - 26 q^{26} - q^{27} + 5 q^{28} - 6 q^{29} + q^{30} + 16 q^{31} + 5 q^{32} - 4 q^{33} + 2 q^{34} - q^{35} + 5 q^{36} + 2 q^{37} + 12 q^{38} - 6 q^{39} - 3 q^{40} - 10 q^{41} + q^{42} + 4 q^{43} + 12 q^{44} - q^{45} + 8 q^{46} + 16 q^{47} + q^{48} + 3 q^{49} + q^{50} + 6 q^{51} + 6 q^{52} - 6 q^{53} + q^{54} - 4 q^{55} - 3 q^{56} - 12 q^{57} - 2 q^{58} + 4 q^{59} + 5 q^{60} - 6 q^{61} + 24 q^{62} + 3 q^{63} - 19 q^{64} - 6 q^{65} + 20 q^{66} - 4 q^{67} - 14 q^{68} + q^{70} + 8 q^{71} - 3 q^{72} - 18 q^{73} + 38 q^{74} - q^{75} + 20 q^{76} + 4 q^{77} + 14 q^{78} + 16 q^{79} + q^{80} + 3 q^{81} - 6 q^{82} - 20 q^{83} - 7 q^{84} + 6 q^{85} - 36 q^{86} + 2 q^{87} - 20 q^{88} - 10 q^{89} + q^{90} - 6 q^{91} + 16 q^{92} - 8 q^{93} - 32 q^{94} - 12 q^{95} + 5 q^{96} - 10 q^{97} + q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(105))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 7
105.2.a.a 105.a 1.a $1$ $0.838$ \(\Q\) None \(1\) \(1\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
105.2.a.b 105.a 1.a $2$ $0.838$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+3q^{4}-q^{5}+\beta q^{6}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(105))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(105)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)