Properties

Label 2016.2.a
Level $2016$
Weight $2$
Character orbit 2016.a
Rep. character $\chi_{2016}(1,\cdot)$
Character field $\Q$
Dimension $30$
Newform subspaces $22$
Sturm bound $768$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(768\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2016))\).

Total New Old
Modular forms 416 30 386
Cusp forms 353 30 323
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.

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(3\)
\(+\)\(+\)\(-\)$-$\(3\)
\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(13\)
Minus space\(-\)\(17\)

Trace form

\( 30 q + 4 q^{5} + O(q^{10}) \) \( 30 q + 4 q^{5} + 4 q^{13} - 20 q^{17} + 18 q^{25} + 4 q^{29} + 4 q^{37} + 12 q^{41} + 30 q^{49} + 52 q^{53} + 4 q^{61} - 40 q^{65} + 12 q^{73} - 8 q^{85} - 4 q^{89} + 28 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2016))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3 7
2016.2.a.a 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.d \(0\) \(0\) \(-2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
2016.2.a.b 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.d \(0\) \(0\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
2016.2.a.c 2016.a 1.a $1$ $16.098$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}-4q^{11}+2q^{13}+4q^{17}-4q^{23}+\cdots\)
2016.2.a.d 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.c \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+2q^{11}-2q^{13}-4q^{17}-4q^{19}+\cdots\)
2016.2.a.e 2016.a 1.a $1$ $16.098$ \(\Q\) None 224.2.a.a \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{11}-4q^{13}+2q^{17}-6q^{19}+\cdots\)
2016.2.a.f 2016.a 1.a $1$ $16.098$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{7}+4q^{11}+2q^{13}-4q^{17}+4q^{23}+\cdots\)
2016.2.a.g 2016.a 1.a $1$ $16.098$ \(\Q\) None 224.2.a.a \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}-4q^{13}+2q^{17}+6q^{19}+\cdots\)
2016.2.a.h 2016.a 1.a $1$ $16.098$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-4q^{11}+2q^{13}-4q^{17}-4q^{23}+\cdots\)
2016.2.a.i 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.c \(0\) \(0\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}-2q^{11}-2q^{13}-4q^{17}+4q^{19}+\cdots\)
2016.2.a.j 2016.a 1.a $1$ $16.098$ \(\Q\) None 2016.2.a.c \(0\) \(0\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{7}+4q^{11}+2q^{13}+4q^{17}+4q^{23}+\cdots\)
2016.2.a.k 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.b \(0\) \(0\) \(2\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-q^{7}+4q^{11}-6q^{13}+2q^{17}+\cdots\)
2016.2.a.l 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.b \(0\) \(0\) \(2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-4q^{11}-6q^{13}+2q^{17}+\cdots\)
2016.2.a.m 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.a \(0\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}-2q^{11}-2q^{13}+4q^{19}+\cdots\)
2016.2.a.n 2016.a 1.a $1$ $16.098$ \(\Q\) None 672.2.a.a \(0\) \(0\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+q^{7}+2q^{11}-2q^{13}-4q^{19}+\cdots\)
2016.2.a.o 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{5}) \) None 224.2.a.c \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(-2-2\beta )q^{11}+\cdots\)
2016.2.a.p 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}-q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots\)
2016.2.a.q 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(-2\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}+(-1-\beta )q^{11}+\cdots\)
2016.2.a.r 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{5}) \) None 224.2.a.c \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+q^{7}+(2+2\beta )q^{11}+\cdots\)
2016.2.a.s 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{3}) \) None 672.2.a.i \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}+2q^{13}+\cdots\)
2016.2.a.t 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{3}) \) None 672.2.a.i \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+(2+\beta )q^{11}+2q^{13}+\cdots\)
2016.2.a.u 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(2\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}-q^{7}+(-1-\beta )q^{11}+2\beta q^{13}+\cdots\)
2016.2.a.v 2016.a 1.a $2$ $16.098$ \(\Q(\sqrt{5}) \) None 2016.2.a.p \(0\) \(0\) \(2\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+q^{7}+(1+\beta )q^{11}+2\beta q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2016)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1008))\)\(^{\oplus 2}\)