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Properties

Label 1440.2.a
Level $1440$
Weight $2$
Character orbit 1440.a
Rep. character $\chi_{1440}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $17$
Sturm bound $576$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1440.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(576\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1440))\).

Total New Old
Modular forms 320 20 300
Cusp forms 257 20 237
Eisenstein series 63 0 63

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
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(3\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)$-$\(4\)
Plus space\(+\)\(7\)
Minus space\(-\)\(13\)

Trace form

\( 20 q + O(q^{10}) \) \( 20 q + 16 q^{13} - 8 q^{17} + 20 q^{25} - 8 q^{29} + 16 q^{37} + 32 q^{41} + 44 q^{49} + 16 q^{53} + 32 q^{61} + 8 q^{65} + 40 q^{73} - 16 q^{77} + 40 q^{89} + 56 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1440))\) 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 3 5
1440.2.a.a 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(-1\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-2q^{13}+6q^{17}+4q^{23}+\cdots\)
1440.2.a.b 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(-1\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots\)
1440.2.a.c 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{13}-6q^{17}-4q^{19}-8q^{23}+\cdots\)
1440.2.a.d 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{13}-6q^{17}+4q^{19}+8q^{23}+\cdots\)
1440.2.a.e 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(-1\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots\)
1440.2.a.f 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-2q^{13}+6q^{17}-4q^{23}+\cdots\)
1440.2.a.g 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
1440.2.a.h 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots\)
1440.2.a.i 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
1440.2.a.j 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}+2q^{13}+2q^{17}+8q^{19}+\cdots\)
1440.2.a.k 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}+2q^{13}+2q^{17}-8q^{19}+\cdots\)
1440.2.a.l 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\)
1440.2.a.m 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots\)
1440.2.a.n 1440.a 1.a $1$ $11.498$ \(\Q\) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots\)
1440.2.a.o 1440.a 1.a $2$ $11.498$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-2\beta q^{11}-2q^{13}-2q^{17}+\cdots\)
1440.2.a.p 1440.a 1.a $2$ $11.498$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}-\beta q^{11}+4q^{13}-2q^{17}+\cdots\)
1440.2.a.q 1440.a 1.a $2$ $11.498$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+\beta q^{11}+4q^{13}+2q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1440))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1440)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(360))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(480))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(720))\)\(^{\oplus 2}\)