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Properties

Label 165.4.m
Level $165$
Weight $4$
Character orbit 165.m
Rep. character $\chi_{165}(16,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $96$
Newform subspaces $4$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
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 304 96 208
Cusp forms 272 96 176
Eisenstein series 32 0 32

Trace form

\( 96 q - 8 q^{2} - 56 q^{4} - 56 q^{7} + 232 q^{8} - 216 q^{9} + O(q^{10}) \) \( 96 q - 8 q^{2} - 56 q^{4} - 56 q^{7} + 232 q^{8} - 216 q^{9} + 160 q^{10} + 172 q^{11} - 56 q^{13} - 708 q^{14} - 1040 q^{16} + 88 q^{17} + 108 q^{18} + 136 q^{19} + 40 q^{20} + 1368 q^{22} + 1472 q^{23} + 540 q^{24} - 600 q^{25} + 408 q^{26} - 772 q^{28} - 1640 q^{29} - 120 q^{30} + 584 q^{31} - 3512 q^{32} - 96 q^{33} - 1328 q^{34} + 520 q^{35} - 504 q^{36} + 24 q^{37} + 1980 q^{38} - 24 q^{39} - 480 q^{40} + 1972 q^{41} + 888 q^{42} + 4416 q^{43} + 632 q^{44} + 172 q^{46} + 1544 q^{47} - 1248 q^{48} + 228 q^{49} - 200 q^{50} + 744 q^{51} - 2708 q^{52} - 3904 q^{53} - 840 q^{55} + 168 q^{56} - 456 q^{57} - 524 q^{58} + 488 q^{59} + 504 q^{61} - 856 q^{62} - 504 q^{63} - 1860 q^{64} + 840 q^{65} - 1932 q^{66} + 1312 q^{68} + 696 q^{69} + 2860 q^{70} - 5232 q^{71} - 2412 q^{72} + 2120 q^{73} + 1212 q^{74} - 7776 q^{76} + 3176 q^{77} + 768 q^{78} + 3892 q^{79} + 320 q^{80} - 1944 q^{81} + 2940 q^{82} + 1480 q^{83} + 5328 q^{84} - 680 q^{85} + 10496 q^{86} + 9456 q^{87} - 5868 q^{88} + 5240 q^{89} - 360 q^{90} + 1700 q^{91} + 2216 q^{92} - 528 q^{93} + 4352 q^{94} - 1980 q^{96} - 576 q^{97} - 3072 q^{98} - 2052 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
165.4.m.a 165.m 11.c $24$ $9.735$ None \(-6\) \(-18\) \(-30\) \(-51\) $\mathrm{SU}(2)[C_{5}]$
165.4.m.b 165.m 11.c $24$ $9.735$ None \(-2\) \(18\) \(30\) \(27\) $\mathrm{SU}(2)[C_{5}]$
165.4.m.c 165.m 11.c $24$ $9.735$ None \(-2\) \(18\) \(-30\) \(-55\) $\mathrm{SU}(2)[C_{5}]$
165.4.m.d 165.m 11.c $24$ $9.735$ None \(2\) \(-18\) \(30\) \(23\) $\mathrm{SU}(2)[C_{5}]$

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

\( S_{4}^{\mathrm{old}}(165, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)