Properties

Label 480.2.a
Level $480$
Weight $2$
Character orbit 480.a
Rep. character $\chi_{480}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $8$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 480.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(7\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(480))\).

Total New Old
Modular forms 112 8 104
Cusp forms 81 8 73
Eisenstein series 31 0 31

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.
\(+\)\(+\)\(+\)\(+\)\(1\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(2\)
Plus space\(+\)\(2\)
Minus space\(-\)\(6\)

Trace form

\( 8q + 8q^{9} + O(q^{10}) \) \( 8q + 8q^{9} + 16q^{13} + 16q^{21} + 8q^{25} + 16q^{37} - 16q^{41} + 8q^{49} - 32q^{53} + 16q^{57} - 16q^{61} - 16q^{65} + 16q^{73} - 32q^{77} + 8q^{81} - 48q^{89} + 16q^{93} - 16q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(480))\) 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
480.2.a.a \(1\) \(3.833\) \(\Q\) None \(0\) \(-1\) \(-1\) \(-4\) \(-\) \(+\) \(+\) \(q-q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
480.2.a.b \(1\) \(3.833\) \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}-q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
480.2.a.c \(1\) \(3.833\) \(\Q\) None \(0\) \(-1\) \(1\) \(-4\) \(-\) \(+\) \(-\) \(q-q^{3}+q^{5}-4q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
480.2.a.d \(1\) \(3.833\) \(\Q\) None \(0\) \(-1\) \(1\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+q^{5}+q^{9}+2q^{13}-q^{15}+6q^{17}+\cdots\)
480.2.a.e \(1\) \(3.833\) \(\Q\) None \(0\) \(1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}-q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
480.2.a.f \(1\) \(3.833\) \(\Q\) None \(0\) \(1\) \(-1\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}-q^{5}+4q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
480.2.a.g \(1\) \(3.833\) \(\Q\) None \(0\) \(1\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+q^{9}+2q^{13}+q^{15}+6q^{17}+\cdots\)
480.2.a.h \(1\) \(3.833\) \(\Q\) None \(0\) \(1\) \(1\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+q^{5}+4q^{7}+q^{9}-2q^{13}+q^{15}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(480))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(480)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)