Properties

Label 108.2.h
Level 108
Weight 2
Character orbit h
Rep. character \(\chi_{108}(35,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 8
Newform subspaces 1
Sturm bound 36
Trace bound 0

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Defining parameters

Level: \( N \) = \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 108.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(108, [\chi])\).

Total New Old
Modular forms 48 16 32
Cusp forms 24 8 16
Eisenstein series 24 8 16

Trace form

\( 8q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 8q + 3q^{2} - q^{4} + 6q^{5} - 8q^{10} - 2q^{13} - 12q^{14} - q^{16} - 18q^{20} + 3q^{22} - 6q^{25} - 12q^{28} - 6q^{29} + 33q^{32} + 7q^{34} - 8q^{37} + 27q^{38} + 10q^{40} - 24q^{41} + 12q^{46} - 10q^{49} - 21q^{50} + 16q^{52} - 18q^{56} + 4q^{58} - 2q^{61} + 26q^{64} + 30q^{65} + 15q^{68} - 6q^{70} + 4q^{73} + 30q^{74} - 3q^{76} + 30q^{77} + 10q^{82} + 8q^{85} - 21q^{86} - 21q^{88} - 24q^{92} - 18q^{94} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(108, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
108.2.h.a \(8\) \(0.862\) 8.0.170772624.1 None \(3\) \(0\) \(6\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{5}-\beta _{7})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(108, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(108, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 3 T + 5 T^{2} - 6 T^{3} + 6 T^{4} - 12 T^{5} + 20 T^{6} - 24 T^{7} + 16 T^{8} \)
$3$ \( \)
$5$ \( ( 1 - 3 T + 11 T^{2} - 24 T^{3} + 54 T^{4} - 120 T^{5} + 275 T^{6} - 375 T^{7} + 625 T^{8} )^{2} \)
$7$ \( 1 + 19 T^{2} + 181 T^{4} + 1558 T^{6} + 12310 T^{8} + 76342 T^{10} + 434581 T^{12} + 2235331 T^{14} + 5764801 T^{16} \)
$11$ \( 1 - 32 T^{2} + 559 T^{4} - 7136 T^{6} + 77680 T^{8} - 863456 T^{10} + 8184319 T^{12} - 56689952 T^{14} + 214358881 T^{16} \)
$13$ \( ( 1 + T - 17 T^{2} - 8 T^{3} + 142 T^{4} - 104 T^{5} - 2873 T^{6} + 2197 T^{7} + 28561 T^{8} )^{2} \)
$17$ \( ( 1 - 61 T^{2} + 1500 T^{4} - 17629 T^{6} + 83521 T^{8} )^{2} \)
$19$ \( ( 1 - 49 T^{2} + 1248 T^{4} - 17689 T^{6} + 130321 T^{8} )^{2} \)
$23$ \( 1 - 77 T^{2} + 3397 T^{4} - 113498 T^{6} + 2994742 T^{8} - 60040442 T^{10} + 950619877 T^{12} - 11398763453 T^{14} + 78310985281 T^{16} \)
$29$ \( ( 1 + 3 T + 59 T^{2} + 168 T^{3} + 2382 T^{4} + 4872 T^{5} + 49619 T^{6} + 73167 T^{7} + 707281 T^{8} )^{2} \)
$31$ \( 1 + 55 T^{2} + 1345 T^{4} - 13310 T^{6} - 1008146 T^{8} - 12790910 T^{10} + 1242135745 T^{12} + 48812702455 T^{14} + 852891037441 T^{16} \)
$37$ \( ( 1 + 2 T + 42 T^{2} + 74 T^{3} + 1369 T^{4} )^{4} \)
$41$ \( ( 1 + 12 T + 131 T^{2} + 996 T^{3} + 7176 T^{4} + 40836 T^{5} + 220211 T^{6} + 827052 T^{7} + 2825761 T^{8} )^{2} \)
$43$ \( 1 + 64 T^{2} - 593 T^{4} + 63424 T^{6} + 10994416 T^{8} + 117270976 T^{10} - 2027348993 T^{12} + 404567235136 T^{14} + 11688200277601 T^{16} \)
$47$ \( 1 - 53 T^{2} + 2053 T^{4} + 194086 T^{6} - 10513226 T^{8} + 428735974 T^{10} + 10017985093 T^{12} - 571298412437 T^{14} + 23811286661761 T^{16} \)
$53$ \( ( 1 - 136 T^{2} + 9054 T^{4} - 382024 T^{6} + 7890481 T^{8} )^{2} \)
$59$ \( 1 - 56 T^{2} - 617 T^{4} + 179704 T^{6} - 8948768 T^{8} + 625549624 T^{10} - 7476411737 T^{12} - 2362109883896 T^{14} + 146830437604321 T^{16} \)
$61$ \( ( 1 + T - 113 T^{2} - 8 T^{3} + 9214 T^{4} - 488 T^{5} - 420473 T^{6} + 226981 T^{7} + 13845841 T^{8} )^{2} \)
$67$ \( 1 + 160 T^{2} + 10255 T^{4} + 1018720 T^{6} + 100399504 T^{8} + 4573034080 T^{10} + 206649745855 T^{12} + 14473341147040 T^{14} + 406067677556641 T^{16} \)
$71$ \( ( 1 + 140 T^{2} + 10230 T^{4} + 705740 T^{6} + 25411681 T^{8} )^{2} \)
$73$ \( ( 1 - T + 138 T^{2} - 73 T^{3} + 5329 T^{4} )^{4} \)
$79$ \( 1 + 115 T^{2} - 2555 T^{4} + 379270 T^{6} + 127521094 T^{8} + 2367024070 T^{10} - 99517456955 T^{12} + 27955057384915 T^{14} + 1517108809906561 T^{16} \)
$83$ \( 1 - 221 T^{2} + 22861 T^{4} - 2696642 T^{6} + 291036430 T^{8} - 18577166738 T^{10} + 1084944676381 T^{12} - 72253822514549 T^{14} + 2252292232139041 T^{16} \)
$89$ \( ( 1 - 184 T^{2} + 21006 T^{4} - 1457464 T^{6} + 62742241 T^{8} )^{2} \)
$97$ \( ( 1 - 2 T - 59 T^{2} + 262 T^{3} - 5828 T^{4} + 25414 T^{5} - 555131 T^{6} - 1825346 T^{7} + 88529281 T^{8} )^{2} \)
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