Properties

Label 105.2.d
Level $105$
Weight $2$
Character orbit 105.d
Rep. character $\chi_{105}(64,\cdot)$
Character field $\Q$
Dimension $8$
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.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
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 \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 20 8 12
Cusp forms 12 8 4
Eisenstein series 8 0 8

Trace form

\( 8 q - 8 q^{4} + 4 q^{5} - 4 q^{6} - 8 q^{9} + O(q^{10}) \) \( 8 q - 8 q^{4} + 4 q^{5} - 4 q^{6} - 8 q^{9} - 8 q^{10} + 4 q^{15} + 24 q^{16} - 28 q^{20} + 4 q^{21} + 12 q^{24} - 8 q^{25} + 24 q^{26} - 12 q^{30} - 16 q^{31} + 32 q^{34} + 4 q^{35} + 8 q^{36} - 8 q^{39} + 16 q^{40} + 8 q^{41} - 32 q^{44} - 4 q^{45} - 16 q^{46} - 8 q^{49} - 8 q^{50} + 8 q^{51} + 4 q^{54} - 8 q^{55} - 24 q^{56} - 16 q^{59} - 4 q^{60} - 16 q^{61} - 40 q^{64} + 24 q^{65} + 8 q^{66} + 8 q^{69} + 8 q^{70} + 32 q^{71} + 80 q^{74} + 16 q^{75} + 16 q^{76} - 32 q^{79} + 44 q^{80} + 8 q^{81} - 12 q^{84} + 16 q^{85} - 40 q^{89} + 8 q^{90} + 16 q^{91} + 32 q^{94} + 16 q^{95} - 68 q^{96} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
105.2.d.a $2$ $0.838$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}+iq^{3}+q^{4}+(1-2i)q^{5}-q^{6}+\cdots\)
105.2.d.b $6$ $0.838$ 6.0.350464.1 None \(0\) \(0\) \(2\) \(0\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{3}+\beta _{5})q^{4}+\cdots\)

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

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