Properties

Label 2280.2.a
Level $2280$
Weight $2$
Character orbit 2280.a
Rep. character $\chi_{2280}(1,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $21$
Sturm bound $960$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2280.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(960\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2280))\).

Total New Old
Modular forms 496 36 460
Cusp forms 465 36 429
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.

\(2\)\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(14\)
Minus space\(-\)\(22\)

Trace form

\( 36 q + 36 q^{9} + O(q^{10}) \) \( 36 q + 36 q^{9} + 36 q^{25} + 8 q^{31} + 8 q^{39} - 8 q^{43} - 48 q^{47} + 36 q^{49} + 16 q^{51} + 8 q^{55} + 4 q^{57} - 32 q^{59} + 8 q^{61} + 32 q^{67} + 24 q^{73} + 32 q^{77} - 40 q^{79} + 36 q^{81} + 48 q^{83} + 8 q^{85} + 48 q^{89} + 48 q^{91} + 16 q^{93} + 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2280))\) 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 19
2280.2.a.a 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-2q^{13}-q^{15}-6q^{17}+\cdots\)
2280.2.a.b 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}+4q^{11}+2q^{13}+\cdots\)
2280.2.a.c 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}-q^{15}+\cdots\)
2280.2.a.d 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(-1\) \(1\) \(2\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+6q^{11}+4q^{13}+\cdots\)
2280.2.a.e 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{7}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2280.2.a.f 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-4q^{11}-2q^{13}+\cdots\)
2280.2.a.g 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(1\) \(1\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2280.2.a.h 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)
2280.2.a.i 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(1\) \(1\) \(4\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2280.2.a.j 2280.a 1.a $1$ $18.206$ \(\Q\) None \(0\) \(1\) \(1\) \(4\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}+2q^{13}+q^{15}+\cdots\)
2280.2.a.k 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}+(-2+\beta )q^{11}+\cdots\)
2280.2.a.l 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-2\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
2280.2.a.m 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(2\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(1+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.n 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{7}) \) None \(0\) \(-2\) \(2\) \(-2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+\beta )q^{7}+q^{9}+(-3+\cdots)q^{11}+\cdots\)
2280.2.a.o 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-2\) \(-4\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(-2+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
2280.2.a.p 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(6\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(3+\beta )q^{7}+q^{9}+(1-\beta )q^{11}+\cdots\)
2280.2.a.q 2280.a 1.a $2$ $18.206$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-6\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+(-3+\beta )q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.r 2280.a 1.a $3$ $18.206$ 3.3.568.1 None \(0\) \(-3\) \(-3\) \(-2\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+(-1-\beta _{2})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
2280.2.a.s 2280.a 1.a $3$ $18.206$ 3.3.316.1 None \(0\) \(-3\) \(3\) \(-2\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+(-1+\beta _{1})q^{7}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
2280.2.a.t 2280.a 1.a $3$ $18.206$ 3.3.1016.1 None \(0\) \(3\) \(-3\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+\beta _{2}q^{7}+q^{9}+(1-\beta _{1}+\cdots)q^{11}+\cdots\)
2280.2.a.u 2280.a 1.a $3$ $18.206$ 3.3.1772.1 None \(0\) \(3\) \(3\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(2+\beta _{2})q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(570))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1140))\)\(^{\oplus 2}\)