Properties

Label 105.4.d
Level $105$
Weight $4$
Character orbit 105.d
Rep. character $\chi_{105}(64,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $2$
Sturm bound $64$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
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: \(64\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 52 16 36
Cusp forms 44 16 28
Eisenstein series 8 0 8

Trace form

\( 16q - 60q^{4} - 28q^{5} - 12q^{6} - 144q^{9} + O(q^{10}) \) \( 16q - 60q^{4} - 28q^{5} - 12q^{6} - 144q^{9} + 8q^{10} - 24q^{15} + 172q^{16} - 72q^{19} + 700q^{20} - 84q^{21} + 324q^{24} - 8q^{25} + 696q^{26} - 1080q^{29} - 432q^{30} - 48q^{31} - 152q^{34} + 56q^{35} + 540q^{36} + 600q^{39} - 2144q^{40} + 1192q^{41} + 32q^{44} + 252q^{45} - 64q^{46} - 784q^{49} - 1288q^{50} - 1560q^{51} + 108q^{54} + 1408q^{55} + 168q^{56} + 352q^{59} - 228q^{60} - 440q^{61} + 1476q^{64} - 3312q^{65} + 1920q^{66} - 1776q^{69} - 756q^{70} + 904q^{71} + 664q^{74} + 528q^{75} + 7840q^{76} + 4880q^{79} - 332q^{80} + 1296q^{81} + 1008q^{84} - 1272q^{85} - 4200q^{86} + 3304q^{89} - 72q^{90} - 1456q^{91} - 9304q^{94} + 440q^{95} + 1236q^{96} + O(q^{100}) \)

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.d.a \(6\) \(6.195\) 6.0.84052224.1 None \(0\) \(0\) \(-14\) \(0\) \(q+\beta _{1}q^{2}-3\beta _{3}q^{3}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
105.4.d.b \(10\) \(6.195\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(0\) \(-14\) \(0\) \(q+\beta _{6}q^{2}-3\beta _{2}q^{3}+(-5-\beta _{1}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)