Properties

Label 2352.2.a
Level $2352$
Weight $2$
Character orbit 2352.a
Rep. character $\chi_{2352}(1,\cdot)$
Character field $\Q$
Dimension $41$
Newform subspaces $33$
Sturm bound $896$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 33 \)
Sturm bound: \(896\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2352))\).

Total New Old
Modular forms 496 41 455
Cusp forms 401 41 360
Eisenstein series 95 0 95

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
\(+\)\(+\)\(+\)$+$\(5\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(7\)
\(+\)\(-\)\(-\)$+$\(3\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(4\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(18\)
Minus space\(-\)\(23\)

Trace form

\( 41 q - q^{3} - 2 q^{5} + 41 q^{9} + O(q^{10}) \) \( 41 q - q^{3} - 2 q^{5} + 41 q^{9} + 4 q^{11} - 2 q^{13} - 2 q^{15} + 2 q^{17} - 12 q^{19} - 8 q^{23} + 47 q^{25} - q^{27} - 10 q^{29} + 4 q^{33} - 10 q^{37} - 6 q^{39} + 10 q^{41} - 2 q^{45} + 24 q^{47} + 2 q^{51} - 2 q^{53} - 4 q^{57} + 28 q^{59} + 14 q^{61} + 20 q^{65} + 32 q^{67} + 8 q^{69} + 32 q^{71} + 10 q^{73} - 15 q^{75} - 12 q^{79} + 41 q^{81} - 20 q^{83} + 12 q^{85} + 18 q^{87} + 10 q^{89} + 8 q^{93} - 32 q^{95} - 14 q^{97} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2352))\) 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 7
2352.2.a.a 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{9}-2q^{11}+6q^{13}+\cdots\)
2352.2.a.b 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{9}+4q^{11}-4q^{13}+\cdots\)
2352.2.a.c 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}-6q^{13}+2q^{15}+\cdots\)
2352.2.a.d 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+2q^{11}+q^{13}+\cdots\)
2352.2.a.e 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+6q^{11}+3q^{13}+\cdots\)
2352.2.a.f 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-5q^{11}+q^{15}+4q^{17}+\cdots\)
2352.2.a.g 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2352.2.a.h 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}+4q^{13}+4q^{17}+4q^{19}+\cdots\)
2352.2.a.i 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2352.2.a.j 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-2q^{11}-4q^{13}+\cdots\)
2352.2.a.k 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}-2q^{11}+3q^{13}+\cdots\)
2352.2.a.l 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{9}+4q^{11}-6q^{13}+\cdots\)
2352.2.a.m 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(-1\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2352.2.a.n 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}+q^{9}-3q^{11}+4q^{13}+\cdots\)
2352.2.a.o 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-2q^{11}-3q^{13}+\cdots\)
2352.2.a.p 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}-2q^{11}+4q^{13}+\cdots\)
2352.2.a.q 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{9}+2q^{13}-2q^{15}+\cdots\)
2352.2.a.r 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}-4q^{13}-4q^{17}-4q^{19}+\cdots\)
2352.2.a.s 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+6q^{11}-2q^{13}-4q^{19}+\cdots\)
2352.2.a.t 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-5q^{11}+q^{15}-4q^{17}+\cdots\)
2352.2.a.u 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+q^{9}-3q^{11}-4q^{13}+\cdots\)
2352.2.a.v 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}-4q^{11}+2q^{13}+\cdots\)
2352.2.a.w 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
2352.2.a.x 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{9}+6q^{11}-3q^{13}+\cdots\)
2352.2.a.y 2352.a 1.a $1$ $18.781$ \(\Q\) None \(0\) \(1\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots\)
2352.2.a.z 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(-2+\beta )q^{5}+q^{9}+(2+2\beta )q^{11}+\cdots\)
2352.2.a.ba 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{57}) \) None \(0\) \(-2\) \(1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}+q^{9}+\beta q^{11}+(-3+\beta )q^{13}+\cdots\)
2352.2.a.bb 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(2+\beta )q^{5}+q^{9}+(-2-2\beta )q^{11}+\cdots\)
2352.2.a.bc 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(2+\beta )q^{5}+q^{9}+2q^{11}+(4+\cdots)q^{13}+\cdots\)
2352.2.a.bd 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+(-2+2\beta )q^{11}+\cdots\)
2352.2.a.be 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(-2+\beta )q^{5}+q^{9}+2q^{11}+\cdots\)
2352.2.a.bf 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{57}) \) None \(0\) \(2\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+q^{9}+\beta q^{11}+(3-\beta )q^{13}+\cdots\)
2352.2.a.bg 2352.a 1.a $2$ $18.781$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+(2+\beta )q^{5}+q^{9}+(2-2\beta )q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2352))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2352)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(336))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(588))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1176))\)\(^{\oplus 2}\)