Properties

Label 150.2.e
Level 150
Weight 2
Character orbit e
Rep. character \(\chi_{150}(107,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 12
Newform subspaces 2
Sturm bound 60
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(150, [\chi])\).

Total New Old
Modular forms 84 12 72
Cusp forms 36 12 24
Eisenstein series 48 0 48

Trace form

\( 12q + 4q^{3} + 8q^{6} + 4q^{7} + O(q^{10}) \) \( 12q + 4q^{3} + 8q^{6} + 4q^{7} - 4q^{12} - 12q^{16} - 8q^{18} - 16q^{21} + 4q^{22} + 4q^{27} + 4q^{28} - 24q^{31} + 4q^{33} + 8q^{36} - 24q^{37} - 4q^{42} - 24q^{43} - 32q^{46} - 4q^{48} - 44q^{51} + 16q^{57} + 20q^{58} + 88q^{61} + 4q^{63} + 44q^{66} + 16q^{67} + 8q^{72} + 20q^{73} + 8q^{76} + 64q^{81} + 16q^{82} - 20q^{87} + 4q^{88} - 8q^{93} - 8q^{96} - 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
150.2.e.a \(4\) \(1.198\) \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(4\) \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
150.2.e.b \(8\) \(1.198\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}+\zeta_{24}^{5})q^{2}+(-2\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T^{4} \))(\( ( 1 + T^{4} )^{2} \))
$3$ (\( 1 - 4 T + 8 T^{2} - 12 T^{3} + 9 T^{4} \))(\( 1 - 9 T^{4} + 81 T^{8} \))
$5$ 1
$7$ (\( ( 1 - 2 T + 2 T^{2} - 14 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 94 T^{4} + 2401 T^{8} )^{2} \))
$11$ (\( ( 1 - 20 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 5 T^{2} + 121 T^{4} )^{4} \))
$13$ (\( ( 1 + 169 T^{4} )^{2} \))(\( ( 1 + 169 T^{4} )^{4} \))
$17$ (\( ( 1 - 16 T^{2} + 289 T^{4} )( 1 + 16 T^{2} + 289 T^{4} ) \))(\( ( 1 + 47 T^{4} + 83521 T^{8} )^{2} \))
$19$ (\( ( 1 - 22 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 37 T^{2} + 361 T^{4} )^{4} \))
$23$ (\( 1 - 158 T^{4} + 279841 T^{8} \))(\( ( 1 - 958 T^{4} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 + 8 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 + 29 T^{2} )^{8} \))
$31$ (\( ( 1 + 2 T + 31 T^{2} )^{4} \))(\( ( 1 + 2 T + 31 T^{2} )^{8} \))
$37$ (\( ( 1 + 12 T + 72 T^{2} + 444 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 1106 T^{4} + 1874161 T^{8} )^{2} \))
$41$ (\( ( 1 - 50 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 55 T^{2} + 1681 T^{4} )^{4} \))
$43$ (\( ( 1 + 12 T + 72 T^{2} + 516 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 + 1778 T^{4} + 3418801 T^{8} )^{2} \))
$47$ (\( ( 1 + 2209 T^{4} )^{2} \))(\( ( 1 + 2209 T^{4} )^{4} \))
$53$ (\( ( 1 - 56 T^{2} + 2809 T^{4} )( 1 + 56 T^{2} + 2809 T^{4} ) \))(\( ( 1 - 718 T^{4} + 7890481 T^{8} )^{2} \))
$59$ (\( ( 1 + 20 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 10 T^{2} + 3481 T^{4} )^{4} \))
$61$ (\( ( 1 + 6 T + 61 T^{2} )^{4} \))(\( ( 1 - 14 T + 61 T^{2} )^{8} \))
$67$ (\( ( 1 - 8 T + 32 T^{2} - 536 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 + 2471 T^{4} + 20151121 T^{8} )^{2} \))
$71$ (\( ( 1 + 58 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 - 71 T^{2} )^{8} \))
$73$ (\( ( 1 - 16 T + 73 T^{2} )^{2}( 1 + 6 T + 73 T^{2} )^{2} \))(\( ( 1 - 5617 T^{4} + 28398241 T^{8} )^{2} \))
$79$ (\( ( 1 - 122 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 + 38 T^{2} + 6241 T^{4} )^{4} \))
$83$ (\( 1 - 13294 T^{4} + 47458321 T^{8} \))(\( ( 1 + 10871 T^{4} + 47458321 T^{8} )^{2} \))
$89$ (\( ( 1 + 170 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 65 T^{2} + 7921 T^{4} )^{4} \))
$97$ (\( ( 1 + 6 T + 18 T^{2} + 582 T^{3} + 9409 T^{4} )^{2} \))(\( ( 1 + 2498 T^{4} + 88529281 T^{8} )^{2} \))
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