Properties

Label 120.2.a
Level $120$
Weight $2$
Character orbit 120.a
Rep. character $\chi_{120}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $2$
Sturm bound $48$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 120.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(120))\).

Total New Old
Modular forms 32 2 30
Cusp forms 17 2 15
Eisenstein series 15 0 15

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)\(5\)FrickeDim.
\(+\)\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2q + 2q^{3} + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 2q + 2q^{3} + 4q^{7} + 2q^{9} - 4q^{11} - 8q^{17} + 4q^{21} - 8q^{23} + 2q^{25} + 2q^{27} - 8q^{29} - 8q^{31} - 4q^{33} - 4q^{35} - 8q^{37} + 4q^{41} + 8q^{43} + 16q^{47} + 2q^{49} - 8q^{51} + 16q^{53} - 4q^{55} + 12q^{59} + 20q^{61} + 4q^{63} + 12q^{65} - 8q^{69} + 8q^{71} - 20q^{73} + 2q^{75} + 8q^{79} + 2q^{81} - 4q^{85} - 8q^{87} + 12q^{89} - 24q^{91} - 8q^{93} - 8q^{95} + 4q^{97} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(120))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5
120.2.a.a \(1\) \(0.958\) \(\Q\) None \(0\) \(1\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}-q^{5}+4q^{7}+q^{9}-6q^{13}-q^{15}+\cdots\)
120.2.a.b \(1\) \(0.958\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}-4q^{11}+6q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(120))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(120)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 - T \))(\( 1 - T \))
$5$ (\( 1 + T \))(\( 1 - T \))
$7$ (\( 1 - 4 T + 7 T^{2} \))(\( 1 + 7 T^{2} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))
$13$ (\( 1 + 6 T + 13 T^{2} \))(\( 1 - 6 T + 13 T^{2} \))
$17$ (\( 1 + 2 T + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))
$19$ (\( 1 - 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))
$23$ (\( 1 + 8 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 2 T + 29 T^{2} \))
$31$ (\( 1 + 31 T^{2} \))(\( 1 + 8 T + 31 T^{2} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))
$41$ (\( 1 - 10 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 - 12 T + 43 T^{2} \))
$47$ (\( 1 - 8 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))
$53$ (\( 1 - 10 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))
$61$ (\( 1 - 6 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))
$67$ (\( 1 + 4 T + 67 T^{2} \))(\( 1 - 4 T + 67 T^{2} \))
$71$ (\( 1 + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))
$73$ (\( 1 + 14 T + 73 T^{2} \))(\( 1 + 6 T + 73 T^{2} \))
$79$ (\( 1 - 16 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))
$89$ (\( 1 - 2 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))
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