Properties

Label 1155.2.l
Level 1155
Weight 2
Character orbit l
Rep. character \(\chi_{1155}(1121,\cdot)\)
Character field \(\Q\)
Dimension 96
Newform subspaces 6
Sturm bound 384
Trace bound 11

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Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(384\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1155, [\chi])\).

Total New Old
Modular forms 200 96 104
Cusp forms 184 96 88
Eisenstein series 16 0 16

Trace form

\( 96q + 8q^{3} + 96q^{4} - 20q^{9} + O(q^{10}) \) \( 96q + 8q^{3} + 96q^{4} - 20q^{9} + 24q^{12} + 4q^{15} + 128q^{16} + 8q^{22} - 96q^{25} - 16q^{27} - 4q^{33} + 32q^{34} - 8q^{36} - 16q^{37} + 56q^{48} - 96q^{49} - 8q^{55} - 64q^{58} + 16q^{60} + 160q^{64} - 60q^{66} - 112q^{67} - 56q^{69} - 8q^{75} - 88q^{78} - 12q^{81} - 16q^{88} - 24q^{91} - 24q^{93} + 80q^{97} - 30q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1155, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1155.2.l.a \(4\) \(9.223\) \(\Q(\zeta_{8})\) None \(-4\) \(4\) \(0\) \(0\) \(q+(-1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
1155.2.l.b \(4\) \(9.223\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.c \(4\) \(9.223\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}+(1-\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(-2\zeta_{8}+\cdots)q^{6}+\cdots\)
1155.2.l.d \(4\) \(9.223\) \(\Q(\zeta_{8})\) None \(4\) \(4\) \(0\) \(0\) \(q+(1-\zeta_{8}^{3})q^{2}+(1+\zeta_{8}^{2})q^{3}+(1-2\zeta_{8}^{3})q^{4}+\cdots\)
1155.2.l.e \(40\) \(9.223\) None \(-4\) \(-4\) \(0\) \(0\)
1155.2.l.f \(40\) \(9.223\) None \(4\) \(-4\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 4 T^{4} )^{2} \))(\( ( 1 + 2 T^{2} + 4 T^{4} )^{2} \))(\( ( 1 - 2 T + 3 T^{2} - 4 T^{3} + 4 T^{4} )^{2} \))
$3$ (\( ( 1 - 2 T + 3 T^{2} )^{2} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))(\( ( 1 - 2 T + 3 T^{2} )^{2} \))
$5$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$7$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{2} \))
$11$ (\( 1 + 14 T^{2} + 121 T^{4} \))(\( ( 1 + 6 T + 11 T^{2} )^{2} \))(\( ( 1 - 6 T + 11 T^{2} )^{2} \))(\( 1 + 14 T^{2} + 121 T^{4} \))
$13$ (\( ( 1 - 13 T^{2} )^{4} \))(\( 1 - 8 T^{2} + 66 T^{4} - 1352 T^{6} + 28561 T^{8} \))(\( 1 - 8 T^{2} + 66 T^{4} - 1352 T^{6} + 28561 T^{8} \))(\( ( 1 - 13 T^{2} )^{4} \))
$17$ (\( ( 1 - 8 T + 42 T^{2} - 136 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 + 6 T + 35 T^{2} + 102 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 - 6 T + 35 T^{2} - 102 T^{3} + 289 T^{4} )^{2} \))(\( ( 1 + 8 T + 42 T^{2} + 136 T^{3} + 289 T^{4} )^{2} \))
$19$ (\( 1 - 52 T^{2} + 1270 T^{4} - 18772 T^{6} + 130321 T^{8} \))(\( 1 - 38 T^{2} + 1011 T^{4} - 13718 T^{6} + 130321 T^{8} \))(\( 1 - 38 T^{2} + 1011 T^{4} - 13718 T^{6} + 130321 T^{8} \))(\( 1 - 52 T^{2} + 1270 T^{4} - 18772 T^{6} + 130321 T^{8} \))
$23$ (\( 1 - 68 T^{2} + 2086 T^{4} - 35972 T^{6} + 279841 T^{8} \))(\( 1 - 38 T^{2} + 771 T^{4} - 20102 T^{6} + 279841 T^{8} \))(\( 1 - 38 T^{2} + 771 T^{4} - 20102 T^{6} + 279841 T^{8} \))(\( 1 - 68 T^{2} + 2086 T^{4} - 35972 T^{6} + 279841 T^{8} \))
$29$ (\( ( 1 + 26 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 6 T + 59 T^{2} - 174 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 6 T + 59 T^{2} + 174 T^{3} + 841 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 + 4 T + 58 T^{2} + 124 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 8 T + 60 T^{2} - 248 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 - 8 T + 60 T^{2} - 248 T^{3} + 961 T^{4} )^{2} \))(\( ( 1 + 4 T + 58 T^{2} + 124 T^{3} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 - 6 T + 37 T^{2} )^{4} \))(\( ( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 8 T + 72 T^{2} - 296 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 - 6 T + 37 T^{2} )^{4} \))
$41$ (\( ( 1 - 4 T + 54 T^{2} - 164 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 12 T + 116 T^{2} + 492 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 - 12 T + 116 T^{2} - 492 T^{3} + 1681 T^{4} )^{2} \))(\( ( 1 + 4 T + 54 T^{2} + 164 T^{3} + 1681 T^{4} )^{2} \))
$43$ (\( 1 - 76 T^{2} + 3094 T^{4} - 140524 T^{6} + 3418801 T^{8} \))(\( 1 - 134 T^{2} + 8115 T^{4} - 247766 T^{6} + 3418801 T^{8} \))(\( 1 - 134 T^{2} + 8115 T^{4} - 247766 T^{6} + 3418801 T^{8} \))(\( 1 - 76 T^{2} + 3094 T^{4} - 140524 T^{6} + 3418801 T^{8} \))
$47$ (\( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \))(\( 1 - 16 T^{2} - 2718 T^{4} - 35344 T^{6} + 4879681 T^{8} \))(\( 1 - 16 T^{2} - 2718 T^{4} - 35344 T^{6} + 4879681 T^{8} \))(\( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \))
$53$ (\( 1 - 188 T^{2} + 14326 T^{4} - 528092 T^{6} + 7890481 T^{8} \))(\( 1 - 190 T^{2} + 14571 T^{4} - 533710 T^{6} + 7890481 T^{8} \))(\( 1 - 190 T^{2} + 14571 T^{4} - 533710 T^{6} + 7890481 T^{8} \))(\( 1 - 188 T^{2} + 14326 T^{4} - 528092 T^{6} + 7890481 T^{8} \))
$59$ (\( 1 - 100 T^{2} + 4854 T^{4} - 348100 T^{6} + 12117361 T^{8} \))(\( 1 - 22 T^{2} + 3555 T^{4} - 76582 T^{6} + 12117361 T^{8} \))(\( 1 - 22 T^{2} + 3555 T^{4} - 76582 T^{6} + 12117361 T^{8} \))(\( 1 - 100 T^{2} + 4854 T^{4} - 348100 T^{6} + 12117361 T^{8} \))
$61$ (\( 1 - 100 T^{2} + 7894 T^{4} - 372100 T^{6} + 13845841 T^{8} \))(\( 1 - 158 T^{2} + 11883 T^{4} - 587918 T^{6} + 13845841 T^{8} \))(\( 1 - 158 T^{2} + 11883 T^{4} - 587918 T^{6} + 13845841 T^{8} \))(\( 1 - 100 T^{2} + 7894 T^{4} - 372100 T^{6} + 13845841 T^{8} \))
$67$ (\( ( 1 - 4 T + 66 T^{2} - 268 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 8 T + 78 T^{2} + 536 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 8 T + 78 T^{2} + 536 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 4 T + 66 T^{2} - 268 T^{3} + 4489 T^{4} )^{2} \))
$71$ (\( 1 - 148 T^{2} + 10950 T^{4} - 746068 T^{6} + 25411681 T^{8} \))(\( 1 - 176 T^{2} + 15234 T^{4} - 887216 T^{6} + 25411681 T^{8} \))(\( 1 - 176 T^{2} + 15234 T^{4} - 887216 T^{6} + 25411681 T^{8} \))(\( 1 - 148 T^{2} + 10950 T^{4} - 746068 T^{6} + 25411681 T^{8} \))
$73$ (\( ( 1 - 2 T^{2} + 5329 T^{4} )^{2} \))(\( 1 - 140 T^{2} + 14406 T^{4} - 746060 T^{6} + 28398241 T^{8} \))(\( 1 - 140 T^{2} + 14406 T^{4} - 746060 T^{6} + 28398241 T^{8} \))(\( ( 1 - 2 T^{2} + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 - 142 T^{2} + 6241 T^{4} )^{2} \))(\( 1 - 272 T^{2} + 30690 T^{4} - 1697552 T^{6} + 38950081 T^{8} \))(\( 1 - 272 T^{2} + 30690 T^{4} - 1697552 T^{6} + 38950081 T^{8} \))(\( ( 1 - 142 T^{2} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 - 12 T + 83 T^{2} )^{4} \))(\( ( 1 - 6 T - 25 T^{2} - 498 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 6 T - 25 T^{2} + 498 T^{3} + 6889 T^{4} )^{2} \))(\( ( 1 + 12 T + 83 T^{2} )^{4} \))
$89$ (\( 1 - 284 T^{2} + 35494 T^{4} - 2249564 T^{6} + 62742241 T^{8} \))(\( 1 + 98 T^{2} + 16443 T^{4} + 776258 T^{6} + 62742241 T^{8} \))(\( 1 + 98 T^{2} + 16443 T^{4} + 776258 T^{6} + 62742241 T^{8} \))(\( 1 - 284 T^{2} + 35494 T^{4} - 2249564 T^{6} + 62742241 T^{8} \))
$97$ (\( ( 1 + 16 T + 250 T^{2} + 1552 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 7 T + 97 T^{2} )^{4} \))(\( ( 1 + 7 T + 97 T^{2} )^{4} \))(\( ( 1 + 16 T + 250 T^{2} + 1552 T^{3} + 9409 T^{4} )^{2} \))
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