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Properties

Label 3146.2.a
Level $3146$
Weight $2$
Character orbit 3146.a
Rep. character $\chi_{3146}(1,\cdot)$
Character field $\Q$
Dimension $109$
Newform subspaces $37$
Sturm bound $924$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3146 = 2 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3146.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(924\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3146))\).

Total New Old
Modular forms 486 109 377
Cusp forms 439 109 330
Eisenstein series 47 0 47

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

\(2\)\(11\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(11\)
\(+\)\(+\)\(-\)$-$\(18\)
\(+\)\(-\)\(+\)$-$\(15\)
\(+\)\(-\)\(-\)$+$\(10\)
\(-\)\(+\)\(+\)$-$\(18\)
\(-\)\(+\)\(-\)$+$\(7\)
\(-\)\(-\)\(+\)$+$\(10\)
\(-\)\(-\)\(-\)$-$\(20\)
Plus space\(+\)\(38\)
Minus space\(-\)\(71\)

Trace form

\( 109 q + q^{2} + 6 q^{3} + 109 q^{4} + 6 q^{5} + 8 q^{7} + q^{8} + 111 q^{9} + O(q^{10}) \) \( 109 q + q^{2} + 6 q^{3} + 109 q^{4} + 6 q^{5} + 8 q^{7} + q^{8} + 111 q^{9} + 4 q^{10} + 6 q^{12} + q^{13} - 2 q^{14} + 109 q^{16} - 8 q^{17} + 5 q^{18} + 4 q^{19} + 6 q^{20} - 4 q^{21} + 12 q^{23} + 133 q^{25} - 3 q^{26} + 18 q^{27} + 8 q^{28} - 18 q^{29} - 2 q^{30} + 16 q^{31} + q^{32} + 10 q^{34} - 30 q^{35} + 111 q^{36} + 30 q^{37} - 8 q^{38} + 4 q^{40} + 2 q^{41} + 22 q^{42} + 18 q^{43} + 34 q^{45} - 4 q^{46} + 16 q^{47} + 6 q^{48} + 139 q^{49} + 23 q^{50} + 22 q^{51} + q^{52} - 14 q^{53} + 12 q^{54} - 2 q^{56} + 40 q^{57} + 30 q^{58} + 16 q^{59} + 30 q^{61} - 4 q^{62} + 40 q^{63} + 109 q^{64} + 28 q^{67} - 8 q^{68} + 52 q^{69} + 4 q^{70} - 24 q^{71} + 5 q^{72} + 18 q^{73} + 4 q^{74} + 40 q^{75} + 4 q^{76} - 2 q^{78} - 4 q^{79} + 6 q^{80} + 125 q^{81} + 34 q^{82} - 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 26 q^{89} - 10 q^{90} + 6 q^{91} + 12 q^{92} - 8 q^{93} - 18 q^{94} - 12 q^{95} + 22 q^{97} - 23 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3146))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11 13
3146.2.a.a 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(-3\) \(-1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{7}+\cdots\)
3146.2.a.b 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(-1\) \(-3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+5q^{7}+\cdots\)
3146.2.a.c 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-3q^{7}+\cdots\)
3146.2.a.d 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(-1\) \(2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+2q^{7}+\cdots\)
3146.2.a.e 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{7}-q^{8}-3q^{9}+\cdots\)
3146.2.a.f 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(1\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-2q^{7}-q^{8}+\cdots\)
3146.2.a.g 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
3146.2.a.h 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(2\) \(-1\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{7}+\cdots\)
3146.2.a.i 3146.a 1.a $1$ $25.121$ \(\Q\) None \(-1\) \(2\) \(1\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+q^{5}-2q^{6}+3q^{7}+\cdots\)
3146.2.a.j 3146.a 1.a $1$ $25.121$ \(\Q\) None \(1\) \(-2\) \(3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+3q^{5}-2q^{6}+q^{7}+\cdots\)
3146.2.a.k 3146.a 1.a $1$ $25.121$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots\)
3146.2.a.l 3146.a 1.a $1$ $25.121$ \(\Q\) None \(1\) \(-1\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-2q^{7}+\cdots\)
3146.2.a.m 3146.a 1.a $1$ $25.121$ \(\Q\) None \(1\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-3q^{9}+\cdots\)
3146.2.a.n 3146.a 1.a $1$ $25.121$ \(\Q\) None \(1\) \(1\) \(-3\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
3146.2.a.o 3146.a 1.a $1$ $25.121$ \(\Q\) None \(1\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}-2q^{7}+q^{8}+\cdots\)
3146.2.a.p 3146.a 1.a $1$ $25.121$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+2q^{7}+q^{8}+\cdots\)
3146.2.a.q 3146.a 1.a $2$ $25.121$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-2\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}-\beta q^{6}+\cdots\)
3146.2.a.r 3146.a 1.a $2$ $25.121$ \(\Q(\sqrt{5}) \) None \(-2\) \(3\) \(-2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\)
3146.2.a.s 3146.a 1.a $2$ $25.121$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(-1-\beta )q^{5}+\beta q^{6}+\cdots\)
3146.2.a.t 3146.a 1.a $2$ $25.121$ \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(-2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-2\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
3146.2.a.u 3146.a 1.a $3$ $25.121$ 3.3.321.1 None \(-3\) \(0\) \(2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
3146.2.a.v 3146.a 1.a $3$ $25.121$ 3.3.321.1 None \(3\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{1}-\beta _{2})q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
3146.2.a.w 3146.a 1.a $3$ $25.121$ 3.3.961.1 None \(3\) \(1\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
3146.2.a.x 3146.a 1.a $4$ $25.121$ 4.4.2525.1 None \(-4\) \(-3\) \(-4\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
3146.2.a.y 3146.a 1.a $4$ $25.121$ 4.4.54332.1 None \(-4\) \(2\) \(1\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{2}q^{6}+\cdots\)
3146.2.a.z 3146.a 1.a $4$ $25.121$ 4.4.88057.1 None \(-4\) \(3\) \(4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
3146.2.a.ba 3146.a 1.a $4$ $25.121$ 4.4.2525.1 None \(4\) \(-3\) \(-4\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
3146.2.a.bb 3146.a 1.a $4$ $25.121$ 4.4.54332.1 None \(4\) \(2\) \(1\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
3146.2.a.bc 3146.a 1.a $4$ $25.121$ 4.4.88057.1 None \(4\) \(3\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
3146.2.a.bd 3146.a 1.a $6$ $25.121$ 6.6.8407625.1 None \(-6\) \(-3\) \(4\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
3146.2.a.be 3146.a 1.a $6$ $25.121$ 6.6.7465625.1 None \(-6\) \(-3\) \(4\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
3146.2.a.bf 3146.a 1.a $6$ $25.121$ 6.6.9880625.1 None \(-6\) \(0\) \(-6\) \(9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
3146.2.a.bg 3146.a 1.a $6$ $25.121$ 6.6.7465625.1 None \(6\) \(-3\) \(4\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
3146.2.a.bh 3146.a 1.a $6$ $25.121$ 6.6.8407625.1 None \(6\) \(-3\) \(4\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
3146.2.a.bi 3146.a 1.a $6$ $25.121$ 6.6.9880625.1 None \(6\) \(0\) \(-6\) \(-9\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(-1-\beta _{1})q^{5}+\cdots\)
3146.2.a.bj 3146.a 1.a $8$ $25.121$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(4\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
3146.2.a.bk 3146.a 1.a $8$ $25.121$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(4\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1})q^{3}+q^{4}+(1-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3146))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3146)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1573))\)\(^{\oplus 2}\)