↑

Properties

Label 3364.2.a
Level $3364$
Weight $2$
Character orbit 3364.a
Rep. character $\chi_{3364}(1,\cdot)$
Character field $\Q$
Dimension $67$
Newform subspaces $18$
Sturm bound $870$
Trace bound $45$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3364 = 2^{2} \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3364.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(870\)
Trace bound: \(45\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3364))\).

Total New Old
Modular forms 480 67 413
Cusp forms 391 67 324
Eisenstein series 89 0 89

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

\(2\)\(29\)FrickeDim
\(-\)\(+\)\(-\)\(37\)
\(-\)\(-\)\(+\)\(30\)
Plus space\(+\)\(30\)
Minus space\(-\)\(37\)

Trace form

\( 67 q - 4 q^{5} - 4 q^{7} + 65 q^{9} + O(q^{10}) \) \( 67 q - 4 q^{5} - 4 q^{7} + 65 q^{9} + 4 q^{11} - 4 q^{13} + 10 q^{15} + 2 q^{17} + 6 q^{19} + 8 q^{21} + 8 q^{23} + 63 q^{25} + 18 q^{27} - 8 q^{31} + 8 q^{35} - 2 q^{37} - 18 q^{39} + 6 q^{41} - 4 q^{43} - 16 q^{45} + 12 q^{47} + 43 q^{49} + 12 q^{51} - 4 q^{53} - 18 q^{55} + 32 q^{57} + 2 q^{59} - 22 q^{61} - 32 q^{63} - 8 q^{65} - 6 q^{67} - 20 q^{69} - 8 q^{71} + 6 q^{73} + 10 q^{75} + 40 q^{77} - 4 q^{79} + 75 q^{81} - 30 q^{83} + 16 q^{85} - 2 q^{89} + 24 q^{91} + 32 q^{93} - 12 q^{95} - 18 q^{97} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3364))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 29
3364.2.a.a 3364.a 1.a $1$ $26.862$ \(\Q\) None 116.2.a.c \(0\) \(-2\) \(-2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+4q^{7}+q^{9}+6q^{11}+\cdots\)
3364.2.a.b 3364.a 1.a $1$ $26.862$ \(\Q\) None 116.2.a.b \(0\) \(-1\) \(3\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-4q^{7}-2q^{9}-3q^{11}+\cdots\)
3364.2.a.c 3364.a 1.a $1$ $26.862$ \(\Q\) None 116.2.a.a \(0\) \(3\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+3q^{5}+4q^{7}+6q^{9}+q^{11}+\cdots\)
3364.2.a.d 3364.a 1.a $2$ $26.862$ \(\Q(\sqrt{5}) \) None 3364.2.a.d \(0\) \(-2\) \(1\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2\beta q^{3}+(2-3\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
3364.2.a.e 3364.a 1.a $2$ $26.862$ \(\Q(\sqrt{13}) \) None 3364.2.a.e \(0\) \(-1\) \(1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+\beta q^{5}+q^{7}+\beta q^{9}+(2+\beta )q^{11}+\cdots\)
3364.2.a.f 3364.a 1.a $2$ $26.862$ \(\Q(\sqrt{7}) \) None 116.2.c.a \(0\) \(0\) \(-2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-2q^{7}+4q^{9}+\beta q^{11}+\cdots\)
3364.2.a.g 3364.a 1.a $2$ $26.862$ \(\Q(\sqrt{13}) \) None 3364.2.a.e \(0\) \(1\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}+q^{7}+\beta q^{9}+(-2-\beta )q^{11}+\cdots\)
3364.2.a.h 3364.a 1.a $2$ $26.862$ \(\Q(\sqrt{5}) \) None 3364.2.a.d \(0\) \(2\) \(1\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+(2-3\beta )q^{5}+(-2+\beta )q^{7}+\cdots\)
3364.2.a.i 3364.a 1.a $3$ $26.862$ \(\Q(\zeta_{14})^+\) None 116.2.g.a \(0\) \(-5\) \(-5\) \(-9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}+(-2+\beta _{1})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3364.2.a.j 3364.a 1.a $3$ $26.862$ \(\Q(\zeta_{14})^+\) None 116.2.g.a \(0\) \(5\) \(-5\) \(-9\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{2})q^{5}+\cdots\)
3364.2.a.k 3364.a 1.a $4$ $26.862$ \(\Q(\zeta_{15})^+\) None 3364.2.a.k \(0\) \(-2\) \(-3\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{1}-2\beta _{3})q^{5}+\cdots\)
3364.2.a.l 3364.a 1.a $4$ $26.862$ \(\Q(\zeta_{15})^+\) None 3364.2.a.k \(0\) \(2\) \(-3\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{3}+(-2+\beta _{1}-2\beta _{3})q^{5}+\cdots\)
3364.2.a.m 3364.a 1.a $6$ $26.862$ 6.6.6456289.1 None 116.2.g.b \(0\) \(-5\) \(10\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{5})q^{5}+\cdots\)
3364.2.a.n 3364.a 1.a $6$ $26.862$ \(\Q(\zeta_{28})^+\) None 116.2.i.a \(0\) \(0\) \(-6\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1-\beta _{2}+\beta _{4})q^{5}+(2-2\beta _{2}+\cdots)q^{7}+\cdots\)
3364.2.a.o 3364.a 1.a $6$ $26.862$ \(\Q(\zeta_{28})^+\) None 116.2.i.b \(0\) \(0\) \(-6\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4})q^{5}+\beta _{4}q^{7}+\cdots\)
3364.2.a.p 3364.a 1.a $6$ $26.862$ 6.6.6456289.1 None 116.2.g.b \(0\) \(5\) \(10\) \(7\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{2}-\beta _{5})q^{5}+(1+\cdots)q^{7}+\cdots\)
3364.2.a.q 3364.a 1.a $8$ $26.862$ 8.8.3266578125.2 None 3364.2.a.q \(0\) \(-4\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{6})q^{3}+(-1+\cdots)q^{5}+\cdots\)
3364.2.a.r 3364.a 1.a $8$ $26.862$ 8.8.3266578125.2 None 3364.2.a.q \(0\) \(4\) \(-1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3}+\beta _{4}+\beta _{5}+\beta _{6})q^{3}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3364))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3364)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(841))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1682))\)\(^{\oplus 2}\)