Properties

Label 189.2.c
Level 189
Weight 2
Character orbit c
Rep. character \(\chi_{189}(188,\cdot)\)
Character field \(\Q\)
Dimension 10
Newform subspaces 3
Sturm bound 48
Trace bound 4

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Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 189.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(48\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(189, [\chi])\).

Total New Old
Modular forms 30 10 20
Cusp forms 18 10 8
Eisenstein series 12 0 12

Trace form

\( 10q - 8q^{4} - 3q^{7} + O(q^{10}) \) \( 10q - 8q^{4} - 3q^{7} - 12q^{16} - 28q^{22} + 22q^{25} + 26q^{28} - 6q^{37} + 12q^{43} - 4q^{46} - 29q^{49} + 80q^{58} + 36q^{64} - 22q^{67} - 36q^{70} - 10q^{79} - 36q^{85} + 4q^{88} + 27q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(189, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
189.2.c.a \(2\) \(1.509\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) \(q+2q^{4}+\zeta_{6}q^{7}+(1-2\zeta_{6})q^{13}+4q^{16}+\cdots\)
189.2.c.b \(4\) \(1.509\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(-8\) \(q-\beta _{1}q^{2}-3q^{4}-\beta _{3}q^{5}+(-2+\beta _{2}+\cdots)q^{7}+\cdots\)
189.2.c.c \(4\) \(1.509\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(4\) \(q-\beta _{1}q^{2}-\beta _{2}q^{5}+(1-\beta _{3})q^{7}-2\beta _{1}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(189, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(189, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T^{2} )^{2} \))(\( ( 1 + T^{2} + 4 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 4 T^{4} )^{2} \))
$3$ 1
$5$ (\( ( 1 + 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 + 7 T^{2} + 25 T^{4} )^{2} \))
$7$ (\( 1 - T + 7 T^{2} \))(\( ( 1 + 4 T + 7 T^{2} )^{2} \))(\( ( 1 - 2 T + 7 T^{2} )^{2} \))
$11$ (\( ( 1 - 11 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 20 T^{2} + 121 T^{4} )^{2} \))
$13$ (\( ( 1 - 5 T + 13 T^{2} )( 1 + 5 T + 13 T^{2} ) \))(\( ( 1 - 14 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 - 20 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( ( 1 + 17 T^{2} )^{2} \))(\( ( 1 + 17 T^{2} )^{4} \))(\( ( 1 + 7 T^{2} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - 7 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 + 16 T^{2} + 361 T^{4} )^{2} \))
$23$ (\( ( 1 - 23 T^{2} )^{2} \))(\( ( 1 - 41 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 529 T^{4} )^{2} \))
$29$ (\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 38 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 8 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} \))(\( ( 1 - 56 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 + 11 T + 37 T^{2} )^{2} \))(\( ( 1 + T + 37 T^{2} )^{4} \))(\( ( 1 - 5 T + 37 T^{2} )^{4} \))
$41$ (\( ( 1 + 41 T^{2} )^{2} \))(\( ( 1 + 67 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 7 T^{2} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 + 8 T + 43 T^{2} )^{2} \))(\( ( 1 - 2 T + 43 T^{2} )^{4} \))(\( ( 1 - 5 T + 43 T^{2} )^{4} \))
$47$ (\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 34 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 19 T^{2} + 2209 T^{4} )^{2} \))
$53$ (\( ( 1 - 53 T^{2} )^{2} \))(\( ( 1 - 26 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 + 22 T^{2} + 2809 T^{4} )^{2} \))
$59$ (\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 58 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 43 T^{2} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 - T + 61 T^{2} )( 1 + T + 61 T^{2} ) \))(\( ( 1 - 14 T + 61 T^{2} )^{2}( 1 + 14 T + 61 T^{2} )^{2} \))(\( ( 1 - 116 T^{2} + 3721 T^{4} )^{2} \))
$67$ (\( ( 1 - 5 T + 67 T^{2} )^{2} \))(\( ( 1 + 10 T + 67 T^{2} )^{4} \))(\( ( 1 - 2 T + 67 T^{2} )^{4} \))
$71$ (\( ( 1 - 71 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 58 T^{2} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 - 7 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( ( 1 - 38 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 - 73 T^{2} )^{4} \))
$79$ (\( ( 1 - 17 T + 79 T^{2} )^{2} \))(\( ( 1 - 2 T + 79 T^{2} )^{4} \))(\( ( 1 + 13 T + 79 T^{2} )^{4} \))
$83$ (\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 106 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 163 T^{2} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 + 89 T^{2} )^{2} \))(\( ( 1 + 43 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 70 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 - 19 T + 97 T^{2} )( 1 + 19 T + 97 T^{2} ) \))(\( ( 1 - 14 T + 97 T^{2} )^{2}( 1 + 14 T + 97 T^{2} )^{2} \))(\( ( 1 + 100 T^{2} + 9409 T^{4} )^{2} \))
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