↑

Properties

Label 2418.2.a
Level $2418$
Weight $2$
Character orbit 2418.a
Rep. character $\chi_{2418}(1,\cdot)$
Character field $\Q$
Dimension $61$
Newform subspaces $19$
Sturm bound $896$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2418 = 2 \cdot 3 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2418.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(896\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2418))\).

Total New Old
Modular forms 456 61 395
Cusp forms 441 61 380
Eisenstein series 15 0 15

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

\(2\)\(3\)\(13\)\(31\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(+\)\(4\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(2\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(6\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(25\)
Minus space\(-\)\(36\)

Trace form

\( 61 q + q^{2} + q^{3} + 61 q^{4} - 10 q^{5} + q^{6} - 8 q^{7} + q^{8} + 61 q^{9} + O(q^{10}) \) \( 61 q + q^{2} + q^{3} + 61 q^{4} - 10 q^{5} + q^{6} - 8 q^{7} + q^{8} + 61 q^{9} + 6 q^{10} - 4 q^{11} + q^{12} + q^{13} + 8 q^{14} + 6 q^{15} + 61 q^{16} - 14 q^{17} + q^{18} - 4 q^{19} - 10 q^{20} + 8 q^{21} + 12 q^{22} - 8 q^{23} + q^{24} + 75 q^{25} + q^{26} + q^{27} - 8 q^{28} + 14 q^{29} + 6 q^{30} + q^{31} + q^{32} + 4 q^{33} + 2 q^{34} + 16 q^{35} + 61 q^{36} + 6 q^{37} + 20 q^{38} + q^{39} + 6 q^{40} + 26 q^{41} - 8 q^{42} + 12 q^{43} - 4 q^{44} - 10 q^{45} + 24 q^{46} - 32 q^{47} + q^{48} + 37 q^{49} + 31 q^{50} + 2 q^{51} + q^{52} + 6 q^{53} + q^{54} - 8 q^{55} + 8 q^{56} - 12 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 18 q^{61} + q^{62} - 8 q^{63} + 61 q^{64} + 6 q^{65} + 12 q^{66} - 20 q^{67} - 14 q^{68} - 24 q^{69} + 32 q^{70} + 8 q^{71} + q^{72} + 26 q^{73} + 6 q^{74} - q^{75} - 4 q^{76} - 16 q^{77} - 3 q^{78} - 40 q^{79} - 10 q^{80} + 61 q^{81} + 18 q^{82} - 12 q^{83} + 8 q^{84} + 44 q^{85} + 12 q^{86} + 6 q^{87} + 12 q^{88} - 6 q^{89} + 6 q^{90} - 8 q^{91} - 8 q^{92} - 3 q^{93} + 32 q^{94} + 24 q^{95} + q^{96} - 102 q^{97} + 25 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2418))\) 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 3 13 31
2418.2.a.a 2418.a 1.a $1$ $19.308$ \(\Q\) None 2418.2.a.a \(-1\) \(1\) \(0\) \(-3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-3q^{7}-q^{8}+\cdots\)
2418.2.a.b 2418.a 1.a $1$ $19.308$ \(\Q\) None 2418.2.a.b \(-1\) \(1\) \(0\) \(-1\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
2418.2.a.c 2418.a 1.a $1$ $19.308$ \(\Q\) None 2418.2.a.c \(1\) \(-1\) \(4\) \(3\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+4q^{5}-q^{6}+3q^{7}+\cdots\)
2418.2.a.d 2418.a 1.a $2$ $19.308$ \(\Q(\sqrt{21}) \) None 2418.2.a.d \(-2\) \(2\) \(-1\) \(3\) $+$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}+(2-\beta )q^{7}+\cdots\)
2418.2.a.e 2418.a 1.a $2$ $19.308$ \(\Q(\sqrt{5}) \) None 2418.2.a.e \(-2\) \(2\) \(5\) \(3\) $+$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(3-\beta )q^{5}-q^{6}+\cdots\)
2418.2.a.f 2418.a 1.a $2$ $19.308$ \(\Q(\sqrt{5}) \) None 2418.2.a.f \(2\) \(-2\) \(-3\) \(-1\) $-$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
2418.2.a.g 2418.a 1.a $2$ $19.308$ \(\Q(\sqrt{5}) \) None 2418.2.a.g \(2\) \(-2\) \(-1\) \(-1\) $-$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}-\beta q^{7}+\cdots\)
2418.2.a.h 2418.a 1.a $2$ $19.308$ \(\Q(\sqrt{13}) \) None 2418.2.a.h \(2\) \(2\) \(-5\) \(-3\) $-$ $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-2-\beta )q^{5}+q^{6}+\cdots\)
2418.2.a.i 2418.a 1.a $2$ $19.308$ \(\Q(\sqrt{5}) \) None 2418.2.a.i \(2\) \(2\) \(-3\) \(-3\) $-$ $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots\)
2418.2.a.j 2418.a 1.a $3$ $19.308$ 3.3.733.1 None 2418.2.a.j \(-3\) \(-3\) \(-3\) \(2\) $+$ $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots\)
2418.2.a.k 2418.a 1.a $4$ $19.308$ 4.4.24197.1 None 2418.2.a.k \(-4\) \(-4\) \(-3\) \(4\) $+$ $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1-\beta _{3})q^{5}+q^{6}+\cdots\)
2418.2.a.l 2418.a 1.a $4$ $19.308$ 4.4.18736.1 None 2418.2.a.l \(-4\) \(-4\) \(0\) \(-10\) $+$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(\beta _{2}-\beta _{3})q^{5}+q^{6}+\cdots\)
2418.2.a.m 2418.a 1.a $4$ $19.308$ 4.4.22896.1 None 2418.2.a.m \(-4\) \(-4\) \(2\) \(-4\) $+$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
2418.2.a.n 2418.a 1.a $4$ $19.308$ 4.4.5744.1 None 2418.2.a.n \(-4\) \(4\) \(-2\) \(0\) $+$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}-q^{6}+\cdots\)
2418.2.a.o 2418.a 1.a $5$ $19.308$ 5.5.2240944.1 None 2418.2.a.o \(-5\) \(5\) \(-6\) \(-2\) $+$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}-q^{6}+\cdots\)
2418.2.a.p 2418.a 1.a $5$ $19.308$ 5.5.17108032.1 None 2418.2.a.p \(5\) \(-5\) \(-2\) \(-1\) $-$ $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+\beta _{2}q^{5}-q^{6}+\beta _{4}q^{7}+\cdots\)
2418.2.a.q 2418.a 1.a $5$ $19.308$ 5.5.25175056.1 None 2418.2.a.q \(5\) \(-5\) \(-2\) \(0\) $-$ $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(\beta _{2}+\cdots)q^{7}+\cdots\)
2418.2.a.r 2418.a 1.a $6$ $19.308$ 6.6.927667520.1 None 2418.2.a.r \(6\) \(6\) \(4\) \(5\) $-$ $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
2418.2.a.s 2418.a 1.a $6$ $19.308$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 2418.2.a.s \(6\) \(6\) \(6\) \(1\) $-$ $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}+q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2418))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2418)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(31))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(62))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(93))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(186))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(403))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(806))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1209))\)\(^{\oplus 2}\)