Properties

Label 1456.2.a
Level $1456$
Weight $2$
Character orbit 1456.a
Rep. character $\chi_{1456}(1,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $22$
Sturm bound $448$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(448\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1456))\).

Total New Old
Modular forms 236 36 200
Cusp forms 213 36 177
Eisenstein series 23 0 23

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(15\)
Minus space\(-\)\(21\)

Trace form

\( 36 q + 2 q^{7} + 44 q^{9} + O(q^{10}) \) \( 36 q + 2 q^{7} + 44 q^{9} - 8 q^{11} - 16 q^{15} + 8 q^{17} + 16 q^{19} + 4 q^{23} + 36 q^{25} - 24 q^{27} - 8 q^{29} + 16 q^{31} - 8 q^{37} + 8 q^{39} - 8 q^{41} + 20 q^{43} - 24 q^{47} + 36 q^{49} + 16 q^{51} - 8 q^{53} + 16 q^{55} - 32 q^{61} + 10 q^{63} + 8 q^{67} - 32 q^{69} + 8 q^{71} + 24 q^{73} + 48 q^{75} - 8 q^{77} + 36 q^{79} + 52 q^{81} - 24 q^{83} - 16 q^{85} + 56 q^{87} + 8 q^{89} - 6 q^{91} + 16 q^{93} - 12 q^{95} + 24 q^{97} - 16 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1456))\) 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 7 13
1456.2.a.a 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(-3\) \(-4\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{5}+q^{7}+6q^{9}-q^{11}+\cdots\)
1456.2.a.b 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(-3\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-q^{7}+6q^{9}+5q^{11}-q^{13}+\cdots\)
1456.2.a.c 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(-2\) \(3\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{5}-q^{7}+q^{9}-q^{13}-6q^{15}+\cdots\)
1456.2.a.d 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}+3q^{11}+q^{13}+\cdots\)
1456.2.a.e 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(-1\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+q^{7}-2q^{9}+q^{11}+q^{13}+\cdots\)
1456.2.a.f 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(0\) \(-3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-q^{7}-3q^{9}+2q^{11}-q^{13}+\cdots\)
1456.2.a.g 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(0\) \(-3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}+q^{7}-3q^{9}+6q^{11}-q^{13}+\cdots\)
1456.2.a.h 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
1456.2.a.i 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(0\) \(2\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+q^{7}-3q^{9}-4q^{11}-q^{13}+\cdots\)
1456.2.a.j 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}-3q^{11}-q^{13}+\cdots\)
1456.2.a.k 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(2\) \(-3\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-3q^{5}-q^{7}+q^{9}+q^{13}-6q^{15}+\cdots\)
1456.2.a.l 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(2\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-q^{7}+q^{9}-4q^{11}-q^{13}+\cdots\)
1456.2.a.m 1456.a 1.a $1$ $11.626$ \(\Q\) None \(0\) \(2\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1456.2.a.n 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+\beta q^{5}-q^{7}+(1-2\beta )q^{9}+\cdots\)
1456.2.a.o 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}+q^{7}+(1+\beta )q^{9}+\cdots\)
1456.2.a.p 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1-\beta )q^{5}+q^{7}+3q^{9}+\cdots\)
1456.2.a.q 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(6\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(3+\beta )q^{5}-q^{7}-q^{9}+3\beta q^{11}+\cdots\)
1456.2.a.r 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+\beta q^{5}+q^{7}+(1+2\beta )q^{9}+\cdots\)
1456.2.a.s 1456.a 1.a $2$ $11.626$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(-2\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+(3+\cdots)q^{9}+\cdots\)
1456.2.a.t 1456.a 1.a $3$ $11.626$ 3.3.316.1 None \(0\) \(2\) \(2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}+\beta _{2})q^{3}+(1-\beta _{1})q^{5}+q^{7}+\cdots\)
1456.2.a.u 1456.a 1.a $4$ $11.626$ 4.4.183064.1 None \(0\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-q^{7}+(2+\beta _{2})q^{9}+\cdots\)
1456.2.a.v 1456.a 1.a $4$ $11.626$ 4.4.64268.1 None \(0\) \(-1\) \(2\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{2})q^{5}+q^{7}+(3+\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1456))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1456)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)