Properties

Label 3179.2.a
Level $3179$
Weight $2$
Character orbit 3179.a
Rep. character $\chi_{3179}(1,\cdot)$
Character field $\Q$
Dimension $226$
Newform subspaces $35$
Sturm bound $612$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 3179 = 11 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3179.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(612\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3179))\).

Total New Old
Modular forms 324 226 98
Cusp forms 289 226 63
Eisenstein series 35 0 35

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

\(11\)\(17\)FrickeDim
\(+\)\(+\)$+$\(49\)
\(+\)\(-\)$-$\(63\)
\(-\)\(+\)$-$\(67\)
\(-\)\(-\)$+$\(47\)
Plus space\(+\)\(96\)
Minus space\(-\)\(130\)

Trace form

\( 226 q - q^{2} + 3 q^{3} + 223 q^{4} - q^{5} + 6 q^{6} + 6 q^{7} + 9 q^{8} + 231 q^{9} + O(q^{10}) \) \( 226 q - q^{2} + 3 q^{3} + 223 q^{4} - q^{5} + 6 q^{6} + 6 q^{7} + 9 q^{8} + 231 q^{9} - 4 q^{10} + 2 q^{11} + 6 q^{12} + 2 q^{13} + 3 q^{15} + 213 q^{16} + 13 q^{18} + 16 q^{20} + 22 q^{21} + q^{22} + 19 q^{23} + 16 q^{24} + 223 q^{25} - 18 q^{26} + 9 q^{27} + 2 q^{29} - 22 q^{30} + 15 q^{31} - 23 q^{32} - q^{33} - 14 q^{35} + 225 q^{36} - 3 q^{37} + 12 q^{38} + 12 q^{39} - 26 q^{40} - 14 q^{41} - 32 q^{42} + 6 q^{43} + q^{44} - 12 q^{45} - 2 q^{46} - 16 q^{47} + 4 q^{48} + 250 q^{49} - 37 q^{50} + 62 q^{52} - 8 q^{53} - 42 q^{54} - q^{55} + 8 q^{56} + 8 q^{57} - 22 q^{58} - 23 q^{59} + 2 q^{60} + 2 q^{61} - 18 q^{62} - 48 q^{63} + 209 q^{64} - 24 q^{65} + 6 q^{66} + 17 q^{67} - 27 q^{69} + 36 q^{70} - 15 q^{71} + 29 q^{72} - 14 q^{73} - 40 q^{74} - 24 q^{75} + 24 q^{76} - 6 q^{77} - 20 q^{78} + 22 q^{79} + 102 q^{80} + 266 q^{81} + 18 q^{82} - 50 q^{83} + 72 q^{84} - 4 q^{86} - 16 q^{87} + 15 q^{88} - 19 q^{89} - 2 q^{90} + 16 q^{91} + 50 q^{92} - 27 q^{93} + 24 q^{94} - 28 q^{95} + 40 q^{96} - 5 q^{97} - 21 q^{98} + 11 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3179))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 11 17
3179.2.a.a 3179.a 1.a $1$ $25.384$ \(\Q\) None \(-2\) \(1\) \(-1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+2q^{7}+\cdots\)
3179.2.a.b 3179.a 1.a $1$ $25.384$ \(\Q\) None \(0\) \(-1\) \(-3\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-3q^{5}-2q^{7}-2q^{9}+\cdots\)
3179.2.a.c 3179.a 1.a $1$ $25.384$ \(\Q\) None \(2\) \(-3\) \(-2\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+2q^{4}-2q^{5}-6q^{6}+\cdots\)
3179.2.a.d 3179.a 1.a $1$ $25.384$ \(\Q\) None \(2\) \(0\) \(-4\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-4q^{5}+5q^{7}-3q^{9}+\cdots\)
3179.2.a.e 3179.a 1.a $1$ $25.384$ \(\Q\) None \(2\) \(0\) \(-1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+2q^{7}-3q^{9}+\cdots\)
3179.2.a.f 3179.a 1.a $1$ $25.384$ \(\Q\) None \(2\) \(0\) \(1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}-2q^{7}-3q^{9}+\cdots\)
3179.2.a.g 3179.a 1.a $1$ $25.384$ \(\Q\) None \(2\) \(3\) \(2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+2q^{4}+2q^{5}+6q^{6}+\cdots\)
3179.2.a.h 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{2}) \) None \(-4\) \(-4\) \(0\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(-2-\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots\)
3179.2.a.i 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{2}) \) None \(-4\) \(4\) \(0\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+(2-\beta )q^{3}+2q^{4}-2\beta q^{5}+\cdots\)
3179.2.a.j 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-1-\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
3179.2.a.k 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(4\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(2-2\beta )q^{4}+\cdots\)
3179.2.a.l 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(-2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
3179.2.a.m 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{2}) \) None \(0\) \(-4\) \(2\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2q^{3}+(1+2\beta )q^{5}-2\beta q^{6}+\cdots\)
3179.2.a.n 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+2q^{3}+(-1-2\beta )q^{5}+2\beta q^{6}+\cdots\)
3179.2.a.o 3179.a 1.a $2$ $25.384$ \(\Q(\sqrt{17}) \) None \(4\) \(1\) \(-1\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+(1-\beta )q^{3}+2q^{4}+(-1+\beta )q^{5}+\cdots\)
3179.2.a.p 3179.a 1.a $3$ $25.384$ 3.3.788.1 None \(-3\) \(-1\) \(-1\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}-q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
3179.2.a.q 3179.a 1.a $3$ $25.384$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(-3\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{1}q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.r 3179.a 1.a $3$ $25.384$ \(\Q(\zeta_{18})^+\) None \(-3\) \(0\) \(3\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.s 3179.a 1.a $3$ $25.384$ 3.3.788.1 None \(-3\) \(1\) \(1\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
3179.2.a.t 3179.a 1.a $3$ $25.384$ 3.3.148.1 None \(-2\) \(3\) \(7\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1+\beta _{2})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.u 3179.a 1.a $3$ $25.384$ 3.3.148.1 None \(1\) \(-3\) \(1\) \(-6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.v 3179.a 1.a $3$ $25.384$ 3.3.148.1 None \(1\) \(3\) \(-1\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
3179.2.a.w 3179.a 1.a $4$ $25.384$ 4.4.33844.1 None \(1\) \(-1\) \(-3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
3179.2.a.x 3179.a 1.a $6$ $25.384$ 6.6.1397493.1 None \(0\) \(-3\) \(3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(-\beta _{1}-\beta _{5})q^{3}+\cdots\)
3179.2.a.y 3179.a 1.a $6$ $25.384$ 6.6.22313961.1 None \(0\) \(0\) \(-6\) \(6\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(\beta _{2}+\beta _{5})q^{4}+\cdots\)
3179.2.a.z 3179.a 1.a $6$ $25.384$ 6.6.22313961.1 None \(0\) \(0\) \(6\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
3179.2.a.ba 3179.a 1.a $6$ $25.384$ 6.6.1397493.1 None \(0\) \(3\) \(-3\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{2}+\beta _{3}+\beta _{5})q^{2}+(\beta _{1}+\beta _{5})q^{3}+\cdots\)
3179.2.a.bb 3179.a 1.a $8$ $25.384$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-2\) \(-4\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
3179.2.a.bc 3179.a 1.a $8$ $25.384$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(2\) \(4\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+\cdots\)
3179.2.a.bd 3179.a 1.a $14$ $25.384$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(0\) \(-8\) \(-12\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
3179.2.a.be 3179.a 1.a $14$ $25.384$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(0\) \(8\) \(12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{9}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
3179.2.a.bf 3179.a 1.a $27$ $25.384$ None \(3\) \(-3\) \(-6\) \(3\) $+$ $-$ $\mathrm{SU}(2)$
3179.2.a.bg 3179.a 1.a $27$ $25.384$ None \(3\) \(3\) \(6\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$
3179.2.a.bh 3179.a 1.a $28$ $25.384$ None \(0\) \(-8\) \(-16\) \(-12\) $-$ $-$ $\mathrm{SU}(2)$
3179.2.a.bi 3179.a 1.a $28$ $25.384$ None \(0\) \(8\) \(16\) \(12\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3179))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3179)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(187))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)