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Properties

Label 2679.2.a
Level $2679$
Weight $2$
Character orbit 2679.a
Rep. character $\chi_{2679}(1,\cdot)$
Character field $\Q$
Dimension $139$
Newform subspaces $16$
Sturm bound $640$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 2679 = 3 \cdot 19 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2679.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(640\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2679))\).

Total New Old
Modular forms 324 139 185
Cusp forms 317 139 178
Eisenstein series 7 0 7

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

\(3\)\(19\)\(47\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(24\)
\(+\)\(-\)\(+\)\(-\)\(24\)
\(+\)\(-\)\(-\)\(+\)\(11\)
\(-\)\(+\)\(+\)\(-\)\(24\)
\(-\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(11\)
\(-\)\(-\)\(-\)\(-\)\(23\)
Plus space\(+\)\(44\)
Minus space\(-\)\(95\)

Trace form

\( 139 q + 9 q^{2} - q^{3} + 145 q^{4} + 10 q^{5} + q^{6} + 8 q^{7} + 21 q^{8} + 139 q^{9} + O(q^{10}) \) \( 139 q + 9 q^{2} - q^{3} + 145 q^{4} + 10 q^{5} + q^{6} + 8 q^{7} + 21 q^{8} + 139 q^{9} - 2 q^{10} + 4 q^{11} - 7 q^{12} + 2 q^{13} + 16 q^{14} + 2 q^{15} + 177 q^{16} + 14 q^{17} + 9 q^{18} - q^{19} + 30 q^{20} - 8 q^{21} - 12 q^{22} - 8 q^{23} - 3 q^{24} + 173 q^{25} + 14 q^{26} - q^{27} + 24 q^{28} + 50 q^{29} + 14 q^{30} - 8 q^{31} + 21 q^{32} + 12 q^{33} + 34 q^{34} - 32 q^{35} + 145 q^{36} + 10 q^{37} - 3 q^{38} - 14 q^{39} + 30 q^{40} + 22 q^{41} + 32 q^{42} - 12 q^{43} + 44 q^{44} + 10 q^{45} + 48 q^{46} - q^{47} + q^{48} + 155 q^{49} + 23 q^{50} + 14 q^{51} - 18 q^{52} + 26 q^{53} + q^{54} - 8 q^{55} + 48 q^{56} - q^{57} + 22 q^{58} + 28 q^{59} + 22 q^{60} + 18 q^{61} - 24 q^{62} + 8 q^{63} + 233 q^{64} + 100 q^{65} - 36 q^{66} - 28 q^{67} + 58 q^{68} + 112 q^{70} + 56 q^{71} + 21 q^{72} + 62 q^{73} + 118 q^{74} - 15 q^{75} - 7 q^{76} + 8 q^{77} - 26 q^{78} - 8 q^{79} + 54 q^{80} + 139 q^{81} - 54 q^{82} - 60 q^{83} - 24 q^{84} - 12 q^{85} + 68 q^{86} - 14 q^{87} + 36 q^{88} - 2 q^{89} - 2 q^{90} + 8 q^{91} - 40 q^{92} - 16 q^{93} - 3 q^{94} - 6 q^{95} + 5 q^{96} + 46 q^{97} + 17 q^{98} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2679))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 19 47
2679.2.a.a 2679.a 1.a $1$ $21.392$ \(\Q\) None 2679.2.a.a \(-2\) \(-1\) \(-3\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-3q^{5}+2q^{6}+\cdots\)
2679.2.a.b 2679.a 1.a $1$ $21.392$ \(\Q\) None 2679.2.a.b \(-2\) \(-1\) \(-1\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}+q^{7}+\cdots\)
2679.2.a.c 2679.a 1.a $1$ $21.392$ \(\Q\) None 2679.2.a.c \(0\) \(1\) \(1\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
2679.2.a.d 2679.a 1.a $1$ $21.392$ \(\Q\) None 2679.2.a.d \(2\) \(-1\) \(-3\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-3q^{5}-2q^{6}+\cdots\)
2679.2.a.e 2679.a 1.a $3$ $21.392$ \(\Q(\zeta_{18})^+\) None 2679.2.a.e \(0\) \(-3\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(-1-\beta _{1}+\cdots)q^{5}+\cdots\)
2679.2.a.f 2679.a 1.a $3$ $21.392$ \(\Q(\zeta_{18})^+\) None 2679.2.a.f \(0\) \(3\) \(-3\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-1+\beta _{2})q^{5}+\cdots\)
2679.2.a.g 2679.a 1.a $4$ $21.392$ 4.4.1957.1 None 2679.2.a.g \(0\) \(-4\) \(5\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{2}-q^{3}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
2679.2.a.h 2679.a 1.a $4$ $21.392$ 4.4.2777.1 None 2679.2.a.h \(0\) \(4\) \(2\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{3}q^{5}+\cdots\)
2679.2.a.i 2679.a 1.a $6$ $21.392$ 6.6.5476681.1 None 2679.2.a.i \(4\) \(-6\) \(-4\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{4})q^{2}-q^{3}+(1+\beta _{2}+2\beta _{4}+\cdots)q^{4}+\cdots\)
2679.2.a.j 2679.a 1.a $7$ $21.392$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 2679.2.a.j \(-4\) \(7\) \(-10\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
2679.2.a.k 2679.a 1.a $7$ $21.392$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 2679.2.a.k \(-2\) \(-7\) \(6\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+(1-\beta _{5}+\cdots)q^{5}+\cdots\)
2679.2.a.l 2679.a 1.a $7$ $21.392$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 2679.2.a.l \(-2\) \(7\) \(-6\) \(7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
2679.2.a.m 2679.a 1.a $23$ $21.392$ None 2679.2.a.m \(2\) \(-23\) \(9\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$
2679.2.a.n 2679.a 1.a $23$ $21.392$ None 2679.2.a.n \(5\) \(23\) \(12\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$
2679.2.a.o 2679.a 1.a $24$ $21.392$ None 2679.2.a.o \(2\) \(-24\) \(-2\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$
2679.2.a.p 2679.a 1.a $24$ $21.392$ None 2679.2.a.p \(6\) \(24\) \(10\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2679))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2679)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(141))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(893))\)\(^{\oplus 2}\)