Properties

Label 105.2.i
Level $105$
Weight $2$
Character orbit 105.i
Rep. character $\chi_{105}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $12$
Newform subspaces $4$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(105, [\chi])\).

Total New Old
Modular forms 40 12 28
Cusp forms 24 12 12
Eisenstein series 16 0 16

Trace form

\( 12q + 4q^{2} + 2q^{3} - 4q^{4} + 2q^{7} - 24q^{8} - 6q^{9} + O(q^{10}) \) \( 12q + 4q^{2} + 2q^{3} - 4q^{4} + 2q^{7} - 24q^{8} - 6q^{9} + 4q^{10} + 4q^{11} + 4q^{12} - 4q^{13} - 4q^{14} - 8q^{16} - 8q^{17} + 4q^{18} - 6q^{19} + 16q^{20} - 12q^{21} + 24q^{22} + 8q^{23} - 12q^{24} - 6q^{25} - 8q^{26} - 4q^{27} + 24q^{28} - 8q^{29} - 6q^{31} + 8q^{32} + 8q^{33} - 16q^{34} + 8q^{35} + 8q^{36} + 10q^{37} + 32q^{38} + 6q^{39} + 12q^{40} + 8q^{41} - 4q^{42} - 44q^{43} + 4q^{44} - 8q^{46} - 8q^{47} - 16q^{48} - 14q^{49} - 8q^{50} + 4q^{51} - 16q^{53} - 24q^{55} - 36q^{56} + 12q^{57} - 20q^{58} + 4q^{59} - 4q^{61} + 24q^{62} + 2q^{63} + 64q^{64} - 12q^{65} - 12q^{66} + 14q^{67} + 12q^{68} + 24q^{69} - 4q^{70} + 32q^{71} + 12q^{72} - 10q^{73} - 4q^{74} + 2q^{75} + 40q^{76} + 44q^{77} + 8q^{78} + 6q^{79} - 16q^{80} - 6q^{81} - 28q^{82} + 8q^{83} + 48q^{84} + 8q^{85} + 20q^{86} + 24q^{87} + 8q^{88} + 16q^{89} - 8q^{90} + 10q^{91} - 88q^{92} - 6q^{93} - 24q^{94} - 24q^{96} - 32q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(105, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
105.2.i.a \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) \(q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
105.2.i.b \(2\) \(0.838\) \(\Q(\sqrt{-3}) \) None \(2\) \(-1\) \(-1\) \(-1\) \(q+2\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
105.2.i.c \(4\) \(0.838\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(2\) \(2\) \(-2\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{5}-\beta _{3}q^{6}+\cdots\)
105.2.i.d \(4\) \(0.838\) \(\Q(\zeta_{12})\) None \(2\) \(2\) \(-2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(105, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(105, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 - 2 T^{2} + 4 T^{4} \))(\( 1 - 2 T + 2 T^{2} - 4 T^{3} + 4 T^{4} \))(\( ( 1 - 2 T^{2} )^{2}( 1 + 2 T^{2} + 4 T^{4} ) \))(\( ( 1 - 2 T + 2 T^{2} )^{2}( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} ) \))
$3$ (\( 1 + T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 - T + T^{2} )^{2} \))
$5$ (\( 1 - T + T^{2} \))(\( 1 + T + T^{2} \))(\( ( 1 - T + T^{2} )^{2} \))(\( ( 1 + T + T^{2} )^{2} \))
$7$ (\( 1 - 5 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 11 T^{2} + 49 T^{4} \))
$11$ (\( 1 - 11 T^{2} + 121 T^{4} \))(\( 1 - 6 T + 25 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 4 T - 8 T^{2} + 8 T^{3} + 279 T^{4} + 88 T^{5} - 968 T^{6} + 5324 T^{7} + 14641 T^{8} \))(\( 1 - 2 T - 16 T^{2} + 4 T^{3} + 235 T^{4} + 44 T^{5} - 1936 T^{6} - 2662 T^{7} + 14641 T^{8} \))
$13$ (\( ( 1 + T + 13 T^{2} )^{2} \))(\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( ( 1 + 6 T + 33 T^{2} + 78 T^{3} + 169 T^{4} )^{2} \))(\( ( 1 - 8 T + 39 T^{2} - 104 T^{3} + 169 T^{4} )^{2} \))
$17$ (\( 1 + 6 T + 19 T^{2} + 102 T^{3} + 289 T^{4} \))(\( 1 - 4 T - T^{2} - 68 T^{3} + 289 T^{4} \))(\( 1 - 4 T - 4 T^{2} + 56 T^{3} - 161 T^{4} + 952 T^{5} - 1156 T^{6} - 19652 T^{7} + 83521 T^{8} \))(\( 1 + 10 T + 44 T^{2} + 220 T^{3} + 1147 T^{4} + 3740 T^{5} + 12716 T^{6} + 49130 T^{7} + 83521 T^{8} \))
$19$ (\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 - 2 T - 3 T^{2} + 62 T^{3} - 388 T^{4} + 1178 T^{5} - 1083 T^{6} - 13718 T^{7} + 130321 T^{8} \))(\( 1 + 2 T - 23 T^{2} - 22 T^{3} + 292 T^{4} - 418 T^{5} - 8303 T^{6} + 13718 T^{7} + 130321 T^{8} \))
$23$ (\( 1 + 6 T + 13 T^{2} + 138 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 7 T^{2} - 92 T^{3} + 529 T^{4} \))(\( 1 - 4 T - 16 T^{2} + 56 T^{3} + 127 T^{4} + 1288 T^{5} - 8464 T^{6} - 48668 T^{7} + 279841 T^{8} \))(\( 1 - 6 T - 16 T^{2} - 36 T^{3} + 1347 T^{4} - 828 T^{5} - 8464 T^{6} - 73002 T^{7} + 279841 T^{8} \))
$29$ (\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 8 T + 29 T^{2} )^{2} \))(\( ( 1 - 8 T + 56 T^{2} - 232 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 - 2 T + 32 T^{2} - 58 T^{3} + 841 T^{4} )^{2} \))
$31$ (\( 1 + 5 T - 6 T^{2} + 155 T^{3} + 961 T^{4} \))(\( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 - 6 T - 27 T^{2} - 6 T^{3} + 1892 T^{4} - 186 T^{5} - 25947 T^{6} - 178746 T^{7} + 923521 T^{8} \))(\( 1 + 6 T - 23 T^{2} - 18 T^{3} + 1404 T^{4} - 558 T^{5} - 22103 T^{6} + 178746 T^{7} + 923521 T^{8} \))
$37$ (\( 1 - 7 T + 12 T^{2} - 259 T^{3} + 1369 T^{4} \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( 1 - 14 T + 75 T^{2} - 658 T^{3} + 6020 T^{4} - 24346 T^{5} + 102675 T^{6} - 709142 T^{7} + 1874161 T^{8} \))(\( 1 + 4 T - 35 T^{2} - 92 T^{3} + 640 T^{4} - 3404 T^{5} - 47915 T^{6} + 202612 T^{7} + 1874161 T^{8} \))
$41$ (\( ( 1 - 12 T + 41 T^{2} )^{2} \))(\( ( 1 + 6 T + 41 T^{2} )^{2} \))(\( ( 1 + 4 T + 68 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 2 T + 80 T^{2} - 82 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 + T + 43 T^{2} )^{2} \))(\( ( 1 - T + 43 T^{2} )^{2} \))(\( ( 1 + 18 T + 165 T^{2} + 774 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 4 T + 63 T^{2} + 172 T^{3} + 1849 T^{4} )^{2} \))
$47$ (\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 46 T^{2} + 496 T^{3} - 2061 T^{4} + 23312 T^{5} + 101614 T^{6} - 415292 T^{7} + 4879681 T^{8} \))(\( ( 1 + 2 T - 43 T^{2} + 94 T^{3} + 2209 T^{4} )^{2} \))
$53$ (\( 1 - 53 T^{2} + 2809 T^{4} \))(\( 1 + 4 T - 37 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 + 8 T - 50 T^{2} + 64 T^{3} + 6795 T^{4} + 3392 T^{5} - 140450 T^{6} + 1191016 T^{7} + 7890481 T^{8} \))(\( 1 + 4 T + 14 T^{2} - 416 T^{3} - 3653 T^{4} - 22048 T^{5} + 39326 T^{6} + 595508 T^{7} + 7890481 T^{8} \))
$59$ (\( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} \))(\( 1 - 8 T + 5 T^{2} - 472 T^{3} + 3481 T^{4} \))(\( 1 - 116 T^{2} + 9975 T^{4} - 403796 T^{6} + 12117361 T^{8} \))(\( 1 + 10 T - 16 T^{2} - 20 T^{3} + 4075 T^{4} - 1180 T^{5} - 55696 T^{6} + 2053790 T^{7} + 12117361 T^{8} \))
$61$ (\( 1 + 2 T - 57 T^{2} + 122 T^{3} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )( 1 - T + 61 T^{2} ) \))(\( 1 + 8 T - 2 T^{2} - 448 T^{3} - 3269 T^{4} - 27328 T^{5} - 7442 T^{6} + 1815848 T^{7} + 13845841 T^{8} \))(\( ( 1 + 4 T - 45 T^{2} + 244 T^{3} + 3721 T^{4} )^{2} \))
$67$ (\( 1 - 7 T - 18 T^{2} - 469 T^{3} + 4489 T^{4} \))(\( 1 + 7 T - 18 T^{2} + 469 T^{3} + 4489 T^{4} \))(\( 1 - 2 T + 31 T^{2} + 322 T^{3} - 4028 T^{4} + 21574 T^{5} + 139159 T^{6} - 601526 T^{7} + 20151121 T^{8} \))(\( 1 - 12 T + 49 T^{2} + 468 T^{3} - 5112 T^{4} + 31356 T^{5} + 219961 T^{6} - 3609156 T^{7} + 20151121 T^{8} \))
$71$ (\( ( 1 - 12 T + 71 T^{2} )^{2} \))(\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( ( 1 + 4 T + 144 T^{2} + 284 T^{3} + 5041 T^{4} )^{2} \))(\( ( 1 - 2 T + 116 T^{2} - 142 T^{3} + 5041 T^{4} )^{2} \))
$73$ (\( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} \))(\( 1 + T - 72 T^{2} + 73 T^{3} + 5329 T^{4} \))(\( 1 - 10 T - 21 T^{2} + 250 T^{3} + 2012 T^{4} + 18250 T^{5} - 111909 T^{6} - 3890170 T^{7} + 28398241 T^{8} \))(\( 1 + 8 T - 23 T^{2} - 472 T^{3} - 2432 T^{4} - 34456 T^{5} - 122567 T^{6} + 3112136 T^{7} + 28398241 T^{8} \))
$79$ (\( ( 1 - 17 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( 1 - T - 78 T^{2} - 79 T^{3} + 6241 T^{4} \))(\( 1 + 2 T - 123 T^{2} - 62 T^{3} + 9572 T^{4} - 4898 T^{5} - 767643 T^{6} + 986078 T^{7} + 38950081 T^{8} \))(\( 1 + 6 T - 23 T^{2} - 594 T^{3} - 5604 T^{4} - 46926 T^{5} - 143543 T^{6} + 2958234 T^{7} + 38950081 T^{8} \))
$83$ (\( ( 1 + 12 T + 83 T^{2} )^{2} \))(\( ( 1 - 2 T + 83 T^{2} )^{2} \))(\( ( 1 - 8 T + 180 T^{2} - 664 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 - 6 T + 28 T^{2} - 498 T^{3} + 6889 T^{4} )^{2} \))
$89$ (\( 1 + 6 T - 53 T^{2} + 534 T^{3} + 7921 T^{4} \))(\( 1 - 12 T + 55 T^{2} - 1068 T^{3} + 7921 T^{4} \))(\( 1 - 16 T + 32 T^{2} - 736 T^{3} + 19471 T^{4} - 65504 T^{5} + 253472 T^{6} - 11279504 T^{7} + 62742241 T^{8} \))(\( 1 + 6 T - 4 T^{2} - 828 T^{3} - 9525 T^{4} - 73692 T^{5} - 31684 T^{6} + 4229814 T^{7} + 62742241 T^{8} \))
$97$ (\( ( 1 + 10 T + 97 T^{2} )^{2} \))(\( ( 1 + 6 T + 97 T^{2} )^{2} \))(\( ( 1 + 16 T + 250 T^{2} + 1552 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 - 16 T + 210 T^{2} - 1552 T^{3} + 9409 T^{4} )^{2} \))
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