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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2366))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 13
2366.2.a.a \(1\) \(18.893\) \(\Q\) None \(-1\) \(-2\) \(-3\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}-2q^{3}+q^{4}-3q^{5}+2q^{6}+q^{7}+\cdots\)
2366.2.a.b \(1\) \(18.893\) \(\Q\) None \(-1\) \(-2\) \(1\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{7}+\cdots\)
2366.2.a.c \(1\) \(18.893\) \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) \(+\) \(-\) \(-\) \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.d \(1\) \(18.893\) \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-2q^{5}+q^{7}-q^{8}-3q^{9}+\cdots\)
2366.2.a.e \(1\) \(18.893\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2366.2.a.f \(1\) \(18.893\) \(\Q\) None \(-1\) \(1\) \(3\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots\)
2366.2.a.g \(1\) \(18.893\) \(\Q\) None \(-1\) \(3\) \(-3\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}-3q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.h \(1\) \(18.893\) \(\Q\) None \(-1\) \(3\) \(4\) \(1\) \(+\) \(-\) \(+\) \(q-q^{2}+3q^{3}+q^{4}+4q^{5}-3q^{6}+q^{7}+\cdots\)
2366.2.a.i \(1\) \(18.893\) \(\Q\) None \(1\) \(-2\) \(-1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{7}+\cdots\)
2366.2.a.j \(1\) \(18.893\) \(\Q\) None \(1\) \(-2\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}-2q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.k \(1\) \(18.893\) \(\Q\) None \(1\) \(-2\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{7}+\cdots\)
2366.2.a.l \(1\) \(18.893\) \(\Q\) None \(1\) \(-1\) \(2\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots\)
2366.2.a.m \(1\) \(18.893\) \(\Q\) None \(1\) \(1\) \(-4\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
2366.2.a.n \(1\) \(18.893\) \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
2366.2.a.o \(1\) \(18.893\) \(\Q\) None \(1\) \(3\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}+3q^{6}-q^{7}+q^{8}+\cdots\)
2366.2.a.p \(1\) \(18.893\) \(\Q\) None \(1\) \(3\) \(3\) \(-1\) \(-\) \(+\) \(+\) \(q+q^{2}+3q^{3}+q^{4}+3q^{5}+3q^{6}-q^{7}+\cdots\)
2366.2.a.q \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(-2\) \(-2\) \(2\) \(2\) \(+\) \(-\) \(-\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(1+\cdots)q^{6}+\cdots\)
2366.2.a.r \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-4\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}+\beta q^{3}+q^{4}+(-2-\beta )q^{5}-\beta q^{6}+\cdots\)
2366.2.a.s \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(-2\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
2366.2.a.t \(2\) \(18.893\) \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(-2\) \(-\) \(+\) \(+\) \(q+q^{2}+\beta q^{3}+q^{4}+(2+\beta )q^{5}+\beta q^{6}+\cdots\)
2366.2.a.u \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-5\) \(-2\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+(-2-\beta _{2})q^{3}+q^{4}-2\beta _{1}q^{5}+\cdots\)
2366.2.a.v \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(-4\) \(-2\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
2366.2.a.w \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(8\) \(3\) \(+\) \(-\) \(+\) \(q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(3+\beta _{2})q^{5}+\cdots\)
2366.2.a.x \(3\) \(18.893\) 3.3.1384.1 None \(-3\) \(1\) \(-2\) \(-3\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
2366.2.a.y \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(-3\) \(2\) \(0\) \(3\) \(+\) \(-\) \(-\) \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(\beta _{1}+\beta _{2})q^{5}+\cdots\)
2366.2.a.z \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(-5\) \(2\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}+(-2-\beta _{2})q^{3}+q^{4}+2\beta _{1}q^{5}+\cdots\)
2366.2.a.ba \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(-4\) \(2\) \(3\) \(-\) \(-\) \(+\) \(q+q^{2}+(-1-\beta _{1})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.bb \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-8\) \(-3\) \(-\) \(+\) \(-\) \(q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-3+\cdots)q^{5}+\cdots\)
2366.2.a.bc \(3\) \(18.893\) 3.3.1384.1 None \(3\) \(1\) \(2\) \(3\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bd \(3\) \(18.893\) \(\Q(\zeta_{14})^+\) None \(3\) \(2\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
2366.2.a.be \(6\) \(18.893\) 6.6.6052921.1 None \(-6\) \(1\) \(-4\) \(-6\) \(+\) \(+\) \(+\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{4})q^{5}+\cdots\)
2366.2.a.bf \(6\) \(18.893\) 6.6.285686784.1 None \(-6\) \(2\) \(2\) \(-6\) \(+\) \(+\) \(-\) \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{1}+\beta _{5})q^{5}+\cdots\)
2366.2.a.bg \(6\) \(18.893\) 6.6.6052921.1 None \(6\) \(1\) \(4\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1-\beta _{4})q^{5}+\beta _{1}q^{6}+\cdots\)
2366.2.a.bh \(6\) \(18.893\) 6.6.285686784.1 None \(6\) \(2\) \(-2\) \(6\) \(-\) \(-\) \(-\) \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{5})q^{5}+\cdots\)

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

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