Properties

Label 99.2.d
Level 99
Weight 2
Character orbit d
Rep. character \(\chi_{99}(98,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 99.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(99, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4q + 4q^{4} + O(q^{10}) \) \( 4q + 4q^{4} - 20q^{16} - 12q^{22} + 12q^{25} - 16q^{31} + 32q^{37} + 4q^{49} - 16q^{55} + 48q^{58} + 4q^{64} - 16q^{67} + 24q^{70} - 48q^{82} + 12q^{88} - 48q^{91} - 40q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(99, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
99.2.d.a \(4\) \(0.791\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+\beta _{2}q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(99, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(99, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T^{2} + 4 T^{4} )^{2} \)
$3$ 1
$5$ \( ( 1 - 8 T^{2} + 25 T^{4} )^{2} \)
$7$ \( ( 1 - 8 T^{2} + 49 T^{4} )^{2} \)
$11$ \( 1 + 10 T^{2} + 121 T^{4} \)
$13$ \( ( 1 - 2 T^{2} + 169 T^{4} )^{2} \)
$17$ \( ( 1 + 17 T^{2} )^{4} \)
$19$ \( ( 1 + 16 T^{2} + 361 T^{4} )^{2} \)
$23$ \( ( 1 - 38 T^{2} + 529 T^{4} )^{2} \)
$29$ \( ( 1 + 10 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 + 4 T + 31 T^{2} )^{4} \)
$37$ \( ( 1 - 8 T + 37 T^{2} )^{4} \)
$41$ \( ( 1 + 34 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 - 80 T^{2} + 1849 T^{4} )^{2} \)
$47$ \( ( 1 - 86 T^{2} + 2209 T^{4} )^{2} \)
$53$ \( ( 1 - 8 T^{2} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 + 10 T^{2} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 - 98 T^{2} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 + 4 T + 67 T^{2} )^{4} \)
$71$ \( ( 1 - 134 T^{2} + 5041 T^{4} )^{2} \)
$73$ \( ( 1 - 73 T^{2} )^{4} \)
$79$ \( ( 1 - 8 T^{2} + 6241 T^{4} )^{2} \)
$83$ \( ( 1 - 26 T^{2} + 6889 T^{4} )^{2} \)
$89$ \( ( 1 - 128 T^{2} + 7921 T^{4} )^{2} \)
$97$ \( ( 1 + 10 T + 97 T^{2} )^{4} \)
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