↑

Properties

Label 2416.2.a
Level $2416$
Weight $2$
Character orbit 2416.a
Rep. character $\chi_{2416}(1,\cdot)$
Character field $\Q$
Dimension $75$
Newform subspaces $18$
Sturm bound $608$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2416 = 2^{4} \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2416.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(608\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2416))\).

Total New Old
Modular forms 310 75 235
Cusp forms 299 75 224
Eisenstein series 11 0 11

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

\(2\)\(151\)FrickeDim
\(+\)\(+\)$+$\(19\)
\(+\)\(-\)$-$\(19\)
\(-\)\(+\)$-$\(22\)
\(-\)\(-\)$+$\(15\)
Plus space\(+\)\(34\)
Minus space\(-\)\(41\)

Trace form

\( 75 q - 2 q^{5} + 71 q^{9} + O(q^{10}) \) \( 75 q - 2 q^{5} + 71 q^{9} + 6 q^{11} - 2 q^{13} + 12 q^{15} - 2 q^{17} + 6 q^{19} - 8 q^{21} + 12 q^{23} + 77 q^{25} + 12 q^{27} - 10 q^{29} - 6 q^{31} - 10 q^{37} - 8 q^{39} - 2 q^{41} - 10 q^{43} - 18 q^{45} + 2 q^{47} + 67 q^{49} - 20 q^{51} - 2 q^{53} - 12 q^{55} + 14 q^{59} - 10 q^{61} + 16 q^{63} + 4 q^{65} - 12 q^{67} - 24 q^{69} - 16 q^{71} - 2 q^{73} + 32 q^{75} - 16 q^{77} + 12 q^{79} + 75 q^{81} - 8 q^{83} - 28 q^{85} - 2 q^{89} - 4 q^{91} - 32 q^{93} + 32 q^{95} - 18 q^{97} - 14 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2416))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 151
2416.2.a.a 2416.a 1.a $1$ $19.292$ \(\Q\) None 302.2.a.a \(0\) \(-2\) \(2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
2416.2.a.b 2416.a 1.a $1$ $19.292$ \(\Q\) None 302.2.a.c \(0\) \(1\) \(-4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+2q^{7}-2q^{9}-2q^{11}+\cdots\)
2416.2.a.c 2416.a 1.a $1$ $19.292$ \(\Q\) None 1208.2.a.a \(0\) \(1\) \(0\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}+2q^{11}+2q^{13}+\cdots\)
2416.2.a.d 2416.a 1.a $1$ $19.292$ \(\Q\) None 302.2.a.b \(0\) \(3\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}+6q^{11}-2q^{13}+\cdots\)
2416.2.a.e 2416.a 1.a $2$ $19.292$ \(\Q(\sqrt{2}) \) None 302.2.a.d \(0\) \(2\) \(0\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(2-2\beta )q^{7}+2\beta q^{9}+(-2+\cdots)q^{11}+\cdots\)
2416.2.a.f 2416.a 1.a $3$ $19.292$ 3.3.257.1 None 151.2.a.b \(0\) \(-6\) \(5\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+(2-\beta _{1}-\beta _{2})q^{5}+2q^{7}+q^{9}+\cdots\)
2416.2.a.g 2416.a 1.a $3$ $19.292$ 3.3.473.1 None 604.2.a.b \(0\) \(0\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}-2\beta _{1}q^{7}-3q^{9}+(2+\cdots)q^{11}+\cdots\)
2416.2.a.h 2416.a 1.a $3$ $19.292$ \(\Q(\zeta_{14})^+\) None 151.2.a.a \(0\) \(1\) \(-7\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-3+\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots\)
2416.2.a.i 2416.a 1.a $3$ $19.292$ 3.3.321.1 None 1208.2.a.b \(0\) \(1\) \(-3\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+(-1+\beta _{1}+\beta _{2})q^{5}+q^{7}+\cdots\)
2416.2.a.j 2416.a 1.a $3$ $19.292$ \(\Q(\zeta_{18})^+\) None 604.2.a.a \(0\) \(3\) \(-3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+2\beta _{1}-\beta _{2})q^{3}+(-1+\beta _{1}-2\beta _{2})q^{5}+\cdots\)
2416.2.a.k 2416.a 1.a $4$ $19.292$ 4.4.6224.1 None 302.2.a.f \(0\) \(-2\) \(0\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2416.2.a.l 2416.a 1.a $4$ $19.292$ 4.4.2777.1 None 1208.2.a.c \(0\) \(-1\) \(-7\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{3}+(-2+\beta _{1})q^{5}+2\beta _{3}q^{7}+\cdots\)
2416.2.a.m 2416.a 1.a $4$ $19.292$ 4.4.25808.1 None 302.2.a.e \(0\) \(0\) \(-4\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-2+\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2416.2.a.n 2416.a 1.a $6$ $19.292$ 6.6.12253129.1 None 604.2.a.c \(0\) \(-3\) \(6\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{4})q^{3}+(1+\beta _{1}+\beta _{5})q^{5}+\cdots\)
2416.2.a.o 2416.a 1.a $6$ $19.292$ 6.6.4838537.1 None 151.2.a.c \(0\) \(5\) \(6\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+(1+\beta _{4})q^{5}+\cdots\)
2416.2.a.p 2416.a 1.a $8$ $19.292$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1208.2.a.d \(0\) \(5\) \(6\) \(9\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-\beta _{4}-\beta _{6})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
2416.2.a.q 2416.a 1.a $11$ $19.292$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 1208.2.a.f \(0\) \(-5\) \(-8\) \(-9\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(\beta _{3}+\beta _{7}+\cdots)q^{7}+\cdots\)
2416.2.a.r 2416.a 1.a $11$ $19.292$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 1208.2.a.e \(0\) \(-3\) \(12\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{3})q^{5}+\beta _{8}q^{7}+(2+\beta _{4}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2416))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2416)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(151))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(302))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(604))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1208))\)\(^{\oplus 2}\)