Properties

Label 4356.2.a
Level $4356$
Weight $2$
Character orbit 4356.a
Rep. character $\chi_{4356}(1,\cdot)$
Character field $\Q$
Dimension $46$
Newform subspaces $26$
Sturm bound $1584$
Trace bound $31$

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Defining parameters

Level: \( N \) \(=\) \( 4356 = 2^{2} \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4356.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(1584\)
Trace bound: \(31\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4356))\).

Total New Old
Modular forms 864 46 818
Cusp forms 721 46 675
Eisenstein series 143 0 143

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

\(2\)\(3\)\(11\)FrickeDim
\(-\)\(+\)\(+\)$-$\(12\)
\(-\)\(+\)\(-\)$+$\(7\)
\(-\)\(-\)\(+\)$+$\(12\)
\(-\)\(-\)\(-\)$-$\(15\)
Plus space\(+\)\(19\)
Minus space\(-\)\(27\)

Trace form

\( 46 q + 2 q^{7} + O(q^{10}) \) \( 46 q + 2 q^{7} - 2 q^{13} + 6 q^{17} - 8 q^{19} - 14 q^{23} + 56 q^{25} - 8 q^{29} + 8 q^{31} - 6 q^{35} + 14 q^{37} + 8 q^{41} - 6 q^{43} - 6 q^{47} + 56 q^{49} + 10 q^{53} + 4 q^{59} - 6 q^{61} + 20 q^{65} + 14 q^{67} + 16 q^{71} + 2 q^{73} + 2 q^{79} + 38 q^{83} + 18 q^{85} - 42 q^{89} + 44 q^{91} - 40 q^{95} + 38 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4356))\) 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 11
4356.2.a.a 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}-2q^{7}-5q^{13}-3q^{17}+4q^{19}+\cdots\)
4356.2.a.b 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(-3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{5}+2q^{7}+5q^{13}+3q^{17}-4q^{19}+\cdots\)
4356.2.a.c 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}-6q^{13}-4q^{17}+2q^{19}+\cdots\)
4356.2.a.d 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}+2q^{13}+4q^{17}+6q^{19}+\cdots\)
4356.2.a.e 4356.a 1.a $1$ $34.783$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q-q^{7}+2q^{13}-q^{19}-5q^{25}-7q^{31}+\cdots\)
4356.2.a.f 4356.a 1.a $1$ $34.783$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q+q^{7}-2q^{13}+q^{19}-5q^{25}-7q^{31}+\cdots\)
4356.2.a.g 4356.a 1.a $1$ $34.783$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $N(\mathrm{U}(1))$ \(q+4q^{7}-2q^{13}-8q^{19}-5q^{25}-4q^{31}+\cdots\)
4356.2.a.h 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+3q^{13}-7q^{17}-4q^{19}+\cdots\)
4356.2.a.i 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-3q^{13}+7q^{17}+4q^{19}+\cdots\)
4356.2.a.j 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{5}-2q^{7}+4q^{13}+6q^{17}-8q^{19}+\cdots\)
4356.2.a.k 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(4\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-5q^{7}-2q^{13}-4q^{17}+3q^{19}+\cdots\)
4356.2.a.l 4356.a 1.a $1$ $34.783$ \(\Q\) None \(0\) \(0\) \(4\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+5q^{7}+2q^{13}+4q^{17}-3q^{19}+\cdots\)
4356.2.a.m 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-2\beta q^{7}+3\beta q^{13}-3\beta q^{17}+\cdots\)
4356.2.a.n 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{33}) \) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(-3\) \(0\) $-$ $-$ $+$ $N(\mathrm{U}(1))$ \(q+(-1-\beta )q^{5}+(-5+\beta )q^{23}+(4+3\beta )q^{25}+\cdots\)
4356.2.a.o 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{7}-\beta q^{19}-6q^{23}-5q^{25}-6\beta q^{29}+\cdots\)
4356.2.a.p 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $N(\mathrm{U}(1))$ \(q+\beta q^{7}-2\beta q^{13}+\beta q^{19}-5q^{25}+\cdots\)
4356.2.a.q 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $N(\mathrm{U}(1))$ \(q-3\beta q^{7}-4\beta q^{13}-5\beta q^{19}-5q^{25}+\cdots\)
4356.2.a.r 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-3+2\beta )q^{7}+(-1-2\beta )q^{13}+\cdots\)
4356.2.a.s 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+3\beta )q^{5}+(-3+2\beta )q^{7}+(3+\cdots)q^{13}+\cdots\)
4356.2.a.t 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(1-3\beta )q^{7}+(4-\beta )q^{13}+(-4+\cdots)q^{17}+\cdots\)
4356.2.a.u 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(-1+3\beta )q^{7}+(-4+\beta )q^{13}+\cdots\)
4356.2.a.v 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+3\beta )q^{5}+(3-2\beta )q^{7}+(-3+\cdots)q^{13}+\cdots\)
4356.2.a.w 4356.a 1.a $2$ $34.783$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+(3-2\beta )q^{7}+(1+2\beta )q^{13}+\cdots\)
4356.2.a.x 4356.a 1.a $4$ $34.783$ 4.4.22000.1 None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-q^{7}+(-3-2\beta _{2})q^{13}+(-\beta _{1}+\cdots)q^{17}+\cdots\)
4356.2.a.y 4356.a 1.a $4$ $34.783$ \(\Q(\sqrt{3}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}-2\beta _{1}q^{7}-\beta _{1}q^{13}+\beta _{3}q^{17}+\cdots\)
4356.2.a.z 4356.a 1.a $4$ $34.783$ 4.4.22000.1 None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+q^{7}+(3+2\beta _{2})q^{13}+(\beta _{1}+\cdots)q^{17}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4356))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4356)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1089))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2178))\)\(^{\oplus 2}\)