Properties

Label 105.4.q
Level $105$
Weight $4$
Character orbit 105.q
Rep. character $\chi_{105}(4,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $48$
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.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
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 104 48 56
Cusp forms 88 48 40
Eisenstein series 16 0 16

Trace form

\( 48q + 96q^{4} - 8q^{5} + 48q^{6} + 216q^{9} + O(q^{10}) \) \( 48q + 96q^{4} - 8q^{5} + 48q^{6} + 216q^{9} + 18q^{10} - 84q^{11} + 84q^{14} - 84q^{15} - 440q^{16} + 308q^{19} - 952q^{20} + 48q^{21} + 288q^{24} + 210q^{25} - 216q^{26} - 288q^{29} + 144q^{30} - 1252q^{31} - 48q^{34} - 1064q^{35} + 1728q^{36} - 168q^{39} - 438q^{40} + 632q^{41} - 416q^{44} + 72q^{45} + 2132q^{46} + 596q^{49} + 4888q^{50} - 168q^{51} + 216q^{54} + 2084q^{55} + 2772q^{56} + 2192q^{59} - 906q^{60} - 1592q^{61} - 12032q^{64} + 660q^{65} - 1740q^{66} - 2112q^{69} - 5130q^{70} - 160q^{71} - 3052q^{74} - 312q^{75} + 4232q^{76} - 588q^{79} - 5944q^{80} - 1944q^{81} + 6012q^{84} + 4328q^{85} - 528q^{86} + 3272q^{89} + 324q^{90} - 5672q^{91} + 3092q^{94} + 5752q^{95} - 5268q^{96} - 1512q^{99} + O(q^{100}) \)

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.q.a \(4\) \(6.195\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) \(q+5\zeta_{12}q^{2}+(-3\zeta_{12}+3\zeta_{12}^{3})q^{3}+\cdots\)
105.4.q.b \(44\) \(6.195\) None \(0\) \(0\) \(-4\) \(0\)

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

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