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Properties

Label 1480.2.a
Level $1480$
Weight $2$
Character orbit 1480.a
Rep. character $\chi_{1480}(1,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $11$
Sturm bound $456$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1480 = 2^{3} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1480.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(456\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1480))\).

Total New Old
Modular forms 236 36 200
Cusp forms 221 36 185
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.

\(2\)\(5\)\(37\)FrickeDim
\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(6\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(5\)
\(-\)\(+\)\(-\)$+$\(5\)
\(-\)\(-\)\(+\)$+$\(5\)
\(-\)\(-\)\(-\)$-$\(4\)
Plus space\(+\)\(15\)
Minus space\(-\)\(21\)

Trace form

\( 36 q - 4 q^{3} - 2 q^{5} + 44 q^{9} + O(q^{10}) \) \( 36 q - 4 q^{3} - 2 q^{5} + 44 q^{9} - 4 q^{11} - 4 q^{13} - 4 q^{17} - 12 q^{19} - 8 q^{21} - 8 q^{23} + 36 q^{25} - 16 q^{27} + 4 q^{29} - 8 q^{31} + 8 q^{33} + 12 q^{35} - 2 q^{37} + 24 q^{39} + 4 q^{41} - 16 q^{43} + 6 q^{45} + 16 q^{47} + 16 q^{49} + 4 q^{53} + 16 q^{57} + 20 q^{59} - 4 q^{61} - 28 q^{67} + 56 q^{69} + 16 q^{71} + 16 q^{73} - 4 q^{75} + 64 q^{77} + 24 q^{79} + 68 q^{81} - 20 q^{83} + 48 q^{89} - 32 q^{91} + 24 q^{93} + 36 q^{97} - 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1480))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 37
1480.2.a.a 1480.a 1.a $1$ $11.818$ \(\Q\) None \(0\) \(-3\) \(-1\) \(-5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{5}-5q^{7}+6q^{9}-3q^{11}+\cdots\)
1480.2.a.b 1480.a 1.a $1$ $11.818$ \(\Q\) None \(0\) \(-2\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+2q^{7}+q^{9}-6q^{13}+\cdots\)
1480.2.a.c 1480.a 1.a $1$ $11.818$ \(\Q\) None \(0\) \(1\) \(1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-q^{7}-2q^{9}-3q^{11}+q^{15}+\cdots\)
1480.2.a.d 1480.a 1.a $1$ $11.818$ \(\Q\) None \(0\) \(2\) \(1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+3q^{7}+q^{9}+3q^{11}+\cdots\)
1480.2.a.e 1480.a 1.a $3$ $11.818$ 3.3.316.1 None \(0\) \(1\) \(-3\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}-\beta _{1}q^{7}+\beta _{2}q^{9}+(-1+\cdots)q^{11}+\cdots\)
1480.2.a.f 1480.a 1.a $3$ $11.818$ 3.3.568.1 None \(0\) \(1\) \(3\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}-\beta _{1}q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
1480.2.a.g 1480.a 1.a $5$ $11.818$ 5.5.583504.1 None \(0\) \(-5\) \(5\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
1480.2.a.h 1480.a 1.a $5$ $11.818$ 5.5.935504.1 None \(0\) \(-1\) \(-5\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+\beta _{3}q^{7}+(\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)
1480.2.a.i 1480.a 1.a $5$ $11.818$ 5.5.6397264.1 None \(0\) \(0\) \(-5\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(1+\beta _{1}-\beta _{3})q^{7}+(1+\cdots)q^{9}+\cdots\)
1480.2.a.j 1480.a 1.a $5$ $11.818$ 5.5.998068.1 None \(0\) \(1\) \(-5\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}-q^{5}-\beta _{2}q^{7}+(2-\beta _{1}-\beta _{2}+\cdots)q^{9}+\cdots\)
1480.2.a.k 1480.a 1.a $6$ $11.818$ 6.6.693982032.1 None \(0\) \(1\) \(6\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+q^{5}+(1+\beta _{2})q^{7}+(2+\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1480))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1480)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(370))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(740))\)\(^{\oplus 2}\)