Properties

Label 105.4.p
Level $105$
Weight $4$
Character orbit 105.p
Rep. character $\chi_{105}(59,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(105, [\chi])\).

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

Trace form

\( 88q - 164q^{4} + O(q^{10}) \) \( 88q - 164q^{4} + 30q^{10} + 114q^{15} - 548q^{16} - 228q^{19} + 300q^{21} + 72q^{24} + 160q^{25} - 318q^{30} + 816q^{31} - 336q^{36} - 336q^{39} + 30q^{40} + 1377q^{45} - 1296q^{46} + 688q^{49} + 138q^{51} + 2268q^{54} - 1866q^{60} + 1392q^{61} + 2248q^{64} - 2772q^{66} + 150q^{70} - 765q^{75} - 1528q^{79} + 2844q^{81} - 5160q^{84} - 1084q^{85} - 5632q^{91} + 4416q^{94} - 3456q^{96} - 660q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.4.p.a \(88\) \(6.195\) None \(0\) \(0\) \(0\) \(0\)