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Properties

Label 2366.2.a
Level $2366$
Weight $2$
Character orbit 2366.a
Rep. character $\chi_{2366}(1,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $34$
Sturm bound $728$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2366.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 34 \)
Sturm bound: \(728\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2366))\).

Total New Old
Modular forms 392 78 314
Cusp forms 337 78 259
Eisenstein series 55 0 55

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

\(2\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(8\)
\(+\)\(+\)\(-\)$-$\(12\)
\(+\)\(-\)\(+\)$-$\(13\)
\(+\)\(-\)\(-\)$+$\(6\)
\(-\)\(+\)\(+\)$-$\(10\)
\(-\)\(+\)\(-\)$+$\(9\)
\(-\)\(-\)\(+\)$+$\(5\)
\(-\)\(-\)\(-\)$-$\(15\)
Plus space\(+\)\(28\)
Minus space\(-\)\(50\)

Trace form

\( 78 q - 6 q^{3} + 78 q^{4} - 2 q^{5} - 2 q^{6} + 78 q^{9} + O(q^{10}) \) \( 78 q - 6 q^{3} + 78 q^{4} - 2 q^{5} - 2 q^{6} + 78 q^{9} + 6 q^{10} + 4 q^{11} - 6 q^{12} + 2 q^{14} + 8 q^{15} + 78 q^{16} + 4 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} - 8 q^{22} + 8 q^{23} - 2 q^{24} + 82 q^{25} - 12 q^{27} + 28 q^{29} + 16 q^{30} - 4 q^{31} + 16 q^{33} + 12 q^{34} + 6 q^{35} + 78 q^{36} - 24 q^{37} + 10 q^{38} + 6 q^{40} + 16 q^{41} + 2 q^{42} + 4 q^{44} + 38 q^{45} + 20 q^{47} - 6 q^{48} + 78 q^{49} - 4 q^{50} + 20 q^{51} + 8 q^{53} + 4 q^{54} + 2 q^{56} + 12 q^{57} + 4 q^{58} + 14 q^{59} + 8 q^{60} - 18 q^{61} - 4 q^{62} - 4 q^{63} + 78 q^{64} - 24 q^{67} + 32 q^{69} - 6 q^{70} - 24 q^{71} + 4 q^{72} - 36 q^{73} + 24 q^{74} - 34 q^{75} - 2 q^{76} + 12 q^{77} + 16 q^{79} - 2 q^{80} + 82 q^{81} + 4 q^{82} + 6 q^{83} + 2 q^{84} - 4 q^{85} - 28 q^{86} + 4 q^{87} - 8 q^{88} + 4 q^{89} + 38 q^{90} + 8 q^{92} - 40 q^{93} - 4 q^{94} - 24 q^{95} - 2 q^{96} - 24 q^{97} + 28 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\) 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 13
2366.2.a.a 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(-2\) \(-3\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots\)
2366.2.a.b 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(-2\) \(1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2366.2.a.c 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.d 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
2366.2.a.e 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2366.2.a.f 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(1\) \(3\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
2366.2.a.g 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(3\) \(-3\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}-3q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.h 2366.a 1.a $1$ $18.893$ \(\Q\) None \(-1\) \(3\) \(4\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.i 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
2366.2.a.j 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.k 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(-2\) \(3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{7}+\cdots\)
2366.2.a.l 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(-1\) \(2\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
2366.2.a.m 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(1\) \(-4\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.n 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2366.2.a.o 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(3\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.p 2366.a 1.a $1$ $18.893$ \(\Q\) None \(1\) \(3\) \(3\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+3q^{5}+3q^{6}-q^{7}+\cdots\)
2366.2.a.q 2366.a 1.a $2$ $18.893$ \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
2366.2.a.r 2366.a 1.a $2$ $18.893$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-4\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-2-\beta )q^{5}-\beta q^{6}+\cdots\)
2366.2.a.s 2366.a 1.a $2$ $18.893$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
2366.2.a.t 2366.a 1.a $2$ $18.893$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}+\beta q^{6}+\cdots\)
2366.2.a.u 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-5\) \(-2\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-2-\beta _{2})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots\)
2366.2.a.v 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(-3\) \(-4\) \(-2\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2366.2.a.w 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(8\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(3+\beta _{2})q^{5}+\cdots\)
2366.2.a.x 2366.a 1.a $3$ $18.893$ 3.3.1384.1 None \(-3\) \(1\) \(-2\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
2366.2.a.y 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(-3\) \(2\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
2366.2.a.z 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(3\) \(-5\) \(2\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-2-\beta _{2})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
2366.2.a.ba 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(3\) \(-4\) \(2\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.bb 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-8\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-3+\cdots)q^{5}+\cdots\)
2366.2.a.bc 2366.a 1.a $3$ $18.893$ 3.3.1384.1 None \(3\) \(1\) \(2\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bd 2366.a 1.a $3$ $18.893$ \(\Q(\zeta_{14})^+\) None \(3\) \(2\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.be 2366.a 1.a $6$ $18.893$ 6.6.6052921.1 None \(-6\) \(1\) \(-4\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
2366.2.a.bf 2366.a 1.a $6$ $18.893$ 6.6.285686784.1 None \(-6\) \(2\) \(2\) \(-6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{5})q^{5}+\cdots\)
2366.2.a.bg 2366.a 1.a $6$ $18.893$ 6.6.6052921.1 None \(6\) \(1\) \(4\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bh 2366.a 1.a $6$ $18.893$ 6.6.285686784.1 None \(6\) \(2\) \(-2\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2366))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2366)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1183))\)\(^{\oplus 2}\)