Properties

Label 3332.2.a
Level $3332$
Weight $2$
Character orbit 3332.a
Rep. character $\chi_{3332}(1,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $21$
Sturm bound $1008$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3332.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(1008\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3332))\).

Total New Old
Modular forms 528 54 474
Cusp forms 481 54 427
Eisenstein series 47 0 47

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

\(2\)\(7\)\(17\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(11\)
\(-\)\(-\)\(-\)\(-\)\(17\)
Plus space\(+\)\(22\)
Minus space\(-\)\(32\)

Trace form

\( 54 q + 2 q^{3} + 4 q^{5} + 58 q^{9} + O(q^{10}) \) \( 54 q + 2 q^{3} + 4 q^{5} + 58 q^{9} + 2 q^{11} + 12 q^{15} + 2 q^{17} + 2 q^{23} + 58 q^{25} + 8 q^{27} + 6 q^{31} - 4 q^{33} + 20 q^{37} + 24 q^{39} + 8 q^{41} + 32 q^{43} + 8 q^{45} - 16 q^{47} - 2 q^{51} - 12 q^{53} + 16 q^{55} + 40 q^{57} + 4 q^{59} + 4 q^{61} + 4 q^{65} + 16 q^{67} + 4 q^{69} + 14 q^{71} - 8 q^{73} - 38 q^{75} + 42 q^{79} + 62 q^{81} + 20 q^{89} - 4 q^{93} - 16 q^{95} + 24 q^{97} - 6 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3332))\) 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 17
3332.2.a.a 3332.a 1.a $1$ $26.606$ \(\Q\) None \(0\) \(-3\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+4q^{5}+6q^{9}+q^{11}+3q^{13}+\cdots\)
3332.2.a.b 3332.a 1.a $1$ $26.606$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}-5q^{11}-5q^{13}-q^{17}+\cdots\)
3332.2.a.c 3332.a 1.a $1$ $26.606$ \(\Q\) None \(0\) \(-1\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}-2q^{9}-3q^{11}+5q^{13}+\cdots\)
3332.2.a.d 3332.a 1.a $1$ $26.606$ \(\Q\) None \(0\) \(1\) \(-4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-2q^{9}-3q^{11}-5q^{13}+\cdots\)
3332.2.a.e 3332.a 1.a $1$ $26.606$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}-5q^{11}+5q^{13}+q^{17}+\cdots\)
3332.2.a.f 3332.a 1.a $1$ $26.606$ \(\Q\) None \(0\) \(3\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{5}+6q^{9}+q^{11}-3q^{13}+\cdots\)
3332.2.a.g 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{5}) \) None \(0\) \(-3\) \(-5\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-2-\beta )q^{5}+(-1+\cdots)q^{9}+\cdots\)
3332.2.a.h 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-2\beta q^{5}+(1-2\beta )q^{9}+\cdots\)
3332.2.a.i 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{21}) \) None \(0\) \(-1\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}+(2+\beta )q^{9}+(2+\cdots)q^{11}+\cdots\)
3332.2.a.j 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-\beta )q^{5}+\beta q^{9}+(-4+2\beta )q^{13}+\cdots\)
3332.2.a.k 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}+\beta q^{9}+4q^{11}+\cdots\)
3332.2.a.l 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}+(-2+\beta )q^{9}+(-4+\cdots)q^{11}+\cdots\)
3332.2.a.m 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{21}) \) None \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-\beta )q^{5}+(2+\beta )q^{9}+(2-2\beta )q^{11}+\cdots\)
3332.2.a.n 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2-\beta )q^{5}+(1+3\beta )q^{9}+\cdots\)
3332.2.a.o 3332.a 1.a $2$ $26.606$ \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2+\beta )q^{5}+(-1+3\beta )q^{9}+\cdots\)
3332.2.a.p 3332.a 1.a $3$ $26.606$ 3.3.257.1 None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+\beta _{2}q^{9}-\beta _{2}q^{11}+\cdots\)
3332.2.a.q 3332.a 1.a $3$ $26.606$ 3.3.257.1 None \(0\) \(1\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+\beta _{2}q^{9}-\beta _{2}q^{11}+\cdots\)
3332.2.a.r 3332.a 1.a $4$ $26.606$ 4.4.113481.1 None \(0\) \(-2\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{1}q^{5}+(3+\beta _{2})q^{9}+\cdots\)
3332.2.a.s 3332.a 1.a $4$ $26.606$ 4.4.113481.1 None \(0\) \(2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-\beta _{1}q^{5}+(3+\beta _{2})q^{9}+\cdots\)
3332.2.a.t 3332.a 1.a $8$ $26.606$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-4\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{7}q^{5}+(1+2\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
3332.2.a.u 3332.a 1.a $8$ $26.606$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(4\) \(4\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{7}q^{5}+(1+2\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(833))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1666))\)\(^{\oplus 2}\)