Properties

Label 30.2.c
Level 30
Weight 2
Character orbit c
Rep. character \(\chi_{30}(19,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 30.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(30, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\( 2q - 2q^{4} - 4q^{5} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} - 4q^{5} + 2q^{6} - 2q^{9} - 2q^{10} + 4q^{11} + 4q^{14} + 2q^{15} + 2q^{16} + 4q^{20} - 4q^{21} - 2q^{24} + 6q^{25} - 12q^{26} - 4q^{30} - 16q^{31} + 4q^{34} + 4q^{35} + 2q^{36} + 12q^{39} + 2q^{40} + 4q^{41} - 4q^{44} + 4q^{45} + 8q^{46} + 6q^{49} + 8q^{50} - 4q^{51} - 2q^{54} - 8q^{55} - 4q^{56} - 20q^{59} - 2q^{60} + 4q^{61} - 2q^{64} - 12q^{65} + 4q^{66} - 8q^{69} - 8q^{70} + 24q^{71} + 4q^{74} - 8q^{75} - 4q^{80} + 2q^{81} + 4q^{84} + 4q^{85} + 8q^{86} + 20q^{89} + 2q^{90} + 24q^{91} - 16q^{94} + 2q^{96} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
30.2.c.a \(2\) \(0.240\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+(-2+i)q^{5}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T^{2} \)
$3$ \( 1 + T^{2} \)
$5$ \( 1 + 4 T + 5 T^{2} \)
$7$ \( 1 - 10 T^{2} + 49 T^{4} \)
$11$ \( ( 1 - 2 T + 11 T^{2} )^{2} \)
$13$ \( ( 1 - 4 T + 13 T^{2} )( 1 + 4 T + 13 T^{2} ) \)
$17$ \( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \)
$19$ \( ( 1 + 19 T^{2} )^{2} \)
$23$ \( 1 - 30 T^{2} + 529 T^{4} \)
$29$ \( ( 1 + 29 T^{2} )^{2} \)
$31$ \( ( 1 + 8 T + 31 T^{2} )^{2} \)
$37$ \( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \)
$41$ \( ( 1 - 2 T + 41 T^{2} )^{2} \)
$43$ \( 1 - 70 T^{2} + 1849 T^{4} \)
$47$ \( 1 - 30 T^{2} + 2209 T^{4} \)
$53$ \( 1 - 70 T^{2} + 2809 T^{4} \)
$59$ \( ( 1 + 10 T + 59 T^{2} )^{2} \)
$61$ \( ( 1 - 2 T + 61 T^{2} )^{2} \)
$67$ \( 1 - 70 T^{2} + 4489 T^{4} \)
$71$ \( ( 1 - 12 T + 71 T^{2} )^{2} \)
$73$ \( 1 - 130 T^{2} + 5329 T^{4} \)
$79$ \( ( 1 + 79 T^{2} )^{2} \)
$83$ \( 1 - 150 T^{2} + 6889 T^{4} \)
$89$ \( ( 1 - 10 T + 89 T^{2} )^{2} \)
$97$ \( ( 1 - 18 T + 97 T^{2} )( 1 + 18 T + 97 T^{2} ) \)
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