Properties

Label 165.4.c
Level $165$
Weight $4$
Character orbit 165.c
Rep. character $\chi_{165}(34,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $2$
Sturm bound $96$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 165.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(165, [\chi])\).

Total New Old
Modular forms 76 28 48
Cusp forms 68 28 40
Eisenstein series 8 0 8

Trace form

\( 28q - 108q^{4} - 28q^{5} - 12q^{6} - 252q^{9} + O(q^{10}) \) \( 28q - 108q^{4} - 28q^{5} - 12q^{6} - 252q^{9} - 76q^{10} - 368q^{14} + 276q^{16} - 168q^{19} + 668q^{20} + 96q^{21} + 324q^{24} - 204q^{25} + 552q^{26} - 1272q^{29} - 336q^{30} - 976q^{31} + 1200q^{34} + 72q^{35} + 972q^{36} + 336q^{39} + 1788q^{40} + 1128q^{41} + 616q^{44} + 252q^{45} - 1344q^{46} + 244q^{49} + 2296q^{50} - 744q^{51} + 108q^{54} - 192q^{56} - 1968q^{59} - 1032q^{60} - 728q^{61} - 2860q^{64} - 3232q^{65} - 528q^{66} + 576q^{69} + 1304q^{70} + 576q^{71} - 1760q^{74} - 216q^{75} + 2192q^{76} - 2744q^{79} - 3116q^{80} + 2268q^{81} - 6048q^{84} + 1440q^{85} - 2528q^{86} + 3064q^{89} + 684q^{90} - 4608q^{91} - 3632q^{94} + 792q^{95} + 6396q^{96} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(165, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
165.4.c.a \(14\) \(9.735\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-14\) \(0\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(-6+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
165.4.c.b \(14\) \(9.735\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(-14\) \(0\) \(q+\beta _{6}q^{2}-\beta _{8}q^{3}+(-2-\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(165, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)