Properties

Label 3822.2.a
Level $3822$
Weight $2$
Character orbit 3822.a
Rep. character $\chi_{3822}(1,\cdot)$
Character field $\Q$
Dimension $82$
Newform subspaces $53$
Sturm bound $1568$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3822.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 53 \)
Sturm bound: \(1568\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\), \(17\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3822))\).

Total New Old
Modular forms 816 82 734
Cusp forms 753 82 671
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.

\(2\)\(3\)\(7\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(6\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(6\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(7\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(34\)
Minus space\(-\)\(48\)

Trace form

\( 82 q + 82 q^{4} - 8 q^{5} - 2 q^{6} + 82 q^{9} + O(q^{10}) \) \( 82 q + 82 q^{4} - 8 q^{5} - 2 q^{6} + 82 q^{9} - 4 q^{10} - 8 q^{11} - 2 q^{13} - 4 q^{15} + 82 q^{16} - 4 q^{17} + 4 q^{19} - 8 q^{20} - 16 q^{22} - 8 q^{23} - 2 q^{24} + 54 q^{25} - 20 q^{29} - 8 q^{30} - 12 q^{31} - 16 q^{34} + 82 q^{36} + 4 q^{37} - 12 q^{38} - 4 q^{40} - 16 q^{43} - 8 q^{44} - 8 q^{45} + 8 q^{46} + 8 q^{47} - 2 q^{52} - 12 q^{53} - 2 q^{54} + 12 q^{57} - 32 q^{59} - 4 q^{60} + 20 q^{61} + 28 q^{62} + 82 q^{64} - 8 q^{65} + 8 q^{66} + 20 q^{67} - 4 q^{68} - 8 q^{69} + 36 q^{73} - 24 q^{74} + 32 q^{75} + 4 q^{76} + 2 q^{78} - 32 q^{79} - 8 q^{80} + 82 q^{81} + 4 q^{82} + 16 q^{85} + 8 q^{86} + 16 q^{87} - 16 q^{88} - 8 q^{89} - 4 q^{90} - 8 q^{92} + 20 q^{93} + 32 q^{94} + 24 q^{95} - 2 q^{96} + 20 q^{97} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3822))\) 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 13
3822.2.a.a 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.b 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.c 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.d 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.e 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.f 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.g 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.h 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.i 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(-1\) \(2\) \(0\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.j 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.k 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-2\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.l 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.m 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.n 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.o 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.p 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.q 3822.a 1.a $1$ $30.519$ \(\Q\) None \(-1\) \(1\) \(2\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.r 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.s 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.t 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.u 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
3822.2.a.v 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.w 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.x 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.y 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.z 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(-1\) \(4\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.ba 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-4\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bb 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bc 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-3\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bd 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.be 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bf 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots\)
3822.2.a.bg 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bh 3822.a 1.a $1$ $30.519$ \(\Q\) None \(1\) \(1\) \(3\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bi 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{7}) \) None \(-2\) \(-2\) \(2\) \(0\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
3822.2.a.bj 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
3822.2.a.bk 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{7}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bl 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.bm 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{57}) \) None \(-2\) \(2\) \(1\) \(0\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
3822.2.a.bn 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-4\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bo 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{17}) \) None \(2\) \(-2\) \(-3\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
3822.2.a.bp 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.bq 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.br 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bs 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bt 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{41}) \) None \(2\) \(2\) \(1\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{8}+\cdots\)
3822.2.a.bu 3822.a 1.a $2$ $30.519$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(4\) \(0\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(2+\beta )q^{5}+q^{6}+\cdots\)
3822.2.a.bv 3822.a 1.a $3$ $30.519$ 3.3.2700.1 None \(-3\) \(-3\) \(3\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)
3822.2.a.bw 3822.a 1.a $3$ $30.519$ 3.3.2700.1 None \(-3\) \(3\) \(-3\) \(0\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}-q^{6}+\cdots\)
3822.2.a.bx 3822.a 1.a $4$ $30.519$ 4.4.10304.1 None \(-4\) \(-4\) \(-6\) \(0\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-2+\beta _{1})q^{5}+q^{6}+\cdots\)
3822.2.a.by 3822.a 1.a $4$ $30.519$ 4.4.10304.1 None \(-4\) \(4\) \(6\) \(0\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots\)
3822.2.a.bz 3822.a 1.a $4$ $30.519$ 4.4.31808.1 None \(4\) \(-4\) \(2\) \(0\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+q^{8}+\cdots\)
3822.2.a.ca 3822.a 1.a $4$ $30.519$ 4.4.31808.1 None \(4\) \(4\) \(-2\) \(0\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3822))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3822)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(273))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(546))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(637))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1274))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1911))\)\(^{\oplus 2}\)