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Properties

Label 8954.2.a
Level $8954$
Weight $2$
Character orbit 8954.a
Rep. character $\chi_{8954}(1,\cdot)$
Character field $\Q$
Dimension $327$
Newform subspaces $48$
Sturm bound $2508$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 8954 = 2 \cdot 11^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8954.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 48 \)
Sturm bound: \(2508\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8954))\).

Total New Old
Modular forms 1278 327 951
Cusp forms 1231 327 904
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.

\(2\)\(11\)\(37\)FrickeDim
\(+\)\(+\)\(+\)$+$\(38\)
\(+\)\(+\)\(-\)$-$\(45\)
\(+\)\(-\)\(+\)$-$\(45\)
\(+\)\(-\)\(-\)$+$\(35\)
\(-\)\(+\)\(+\)$-$\(46\)
\(-\)\(+\)\(-\)$+$\(33\)
\(-\)\(-\)\(+\)$+$\(35\)
\(-\)\(-\)\(-\)$-$\(50\)
Plus space\(+\)\(141\)
Minus space\(-\)\(186\)

Trace form

\( 327 q + q^{2} + 2 q^{3} + 327 q^{4} + 2 q^{5} + 8 q^{7} + q^{8} + 333 q^{9} + O(q^{10}) \) \( 327 q + q^{2} + 2 q^{3} + 327 q^{4} + 2 q^{5} + 8 q^{7} + q^{8} + 333 q^{9} + 4 q^{10} + 2 q^{12} + 14 q^{13} - 4 q^{14} + 327 q^{16} + 6 q^{17} + 5 q^{18} + 16 q^{19} + 2 q^{20} - 4 q^{21} - 4 q^{23} + 335 q^{25} + 12 q^{26} - 4 q^{27} + 8 q^{28} + 6 q^{29} + 12 q^{31} + q^{32} + 6 q^{34} + 12 q^{35} + 333 q^{36} - q^{37} + 20 q^{38} + 28 q^{39} + 4 q^{40} - 4 q^{41} + 8 q^{42} + 16 q^{43} + 10 q^{45} - 22 q^{46} - 4 q^{47} + 2 q^{48} + 351 q^{49} - q^{50} - 8 q^{51} + 14 q^{52} + 14 q^{53} + 24 q^{54} - 4 q^{56} - 28 q^{57} + 20 q^{58} + 32 q^{59} - 2 q^{61} + 14 q^{62} + 12 q^{63} + 327 q^{64} - 32 q^{65} + 34 q^{67} + 6 q^{68} - 16 q^{69} + 20 q^{70} - 8 q^{71} + 5 q^{72} + 8 q^{73} + 5 q^{74} - 16 q^{75} + 16 q^{76} - 10 q^{78} + 4 q^{79} + 2 q^{80} + 335 q^{81} + 26 q^{82} - 20 q^{83} - 4 q^{84} - 4 q^{85} + 16 q^{86} - 12 q^{87} + 2 q^{89} + 2 q^{90} - 8 q^{91} - 4 q^{92} - 40 q^{93} - 24 q^{94} - 36 q^{95} - 2 q^{97} - 7 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8954))\) 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 37
8954.2.a.a 8954.a 1.a $1$ $71.498$ \(\Q\) None \(-1\) \(-2\) \(-1\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-q^{5}+2q^{6}+4q^{7}+\cdots\)
8954.2.a.b 8954.a 1.a $1$ $71.498$ \(\Q\) None \(-1\) \(-2\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{6}-4q^{7}-q^{8}+\cdots\)
8954.2.a.c 8954.a 1.a $1$ $71.498$ \(\Q\) None \(-1\) \(0\) \(-1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+4q^{7}-q^{8}-3q^{9}+\cdots\)
8954.2.a.d 8954.a 1.a $1$ $71.498$ \(\Q\) None \(-1\) \(2\) \(3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+3q^{5}-2q^{6}-q^{8}+\cdots\)
8954.2.a.e 8954.a 1.a $1$ $71.498$ \(\Q\) None \(1\) \(-2\) \(-3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-3q^{5}-2q^{6}-2q^{7}+\cdots\)
8954.2.a.f 8954.a 1.a $1$ $71.498$ \(\Q\) None \(1\) \(-2\) \(-1\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}-4q^{7}+\cdots\)
8954.2.a.g 8954.a 1.a $1$ $71.498$ \(\Q\) None \(1\) \(-2\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-2q^{6}+4q^{7}+q^{8}+\cdots\)
8954.2.a.h 8954.a 1.a $1$ $71.498$ \(\Q\) None \(1\) \(2\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+3q^{5}+2q^{6}+q^{8}+\cdots\)
8954.2.a.i 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{2}) \) None \(-2\) \(-4\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-2+\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
8954.2.a.j 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{5}) \) None \(-2\) \(-1\) \(1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+(-1+3\beta )q^{5}+\cdots\)
8954.2.a.k 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(-6\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+(-3+\beta )q^{5}-\beta q^{6}+\cdots\)
8954.2.a.l 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(5\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(3-\beta )q^{5}+\cdots\)
8954.2.a.m 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(-6\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(-3+\beta )q^{5}+\beta q^{6}+\cdots\)
8954.2.a.n 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(1-\beta )q^{5}+\beta q^{6}+\cdots\)
8954.2.a.o 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(5\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-2\beta )q^{3}+q^{4}+(3-\beta )q^{5}+\cdots\)
8954.2.a.p 8954.a 1.a $2$ $71.498$ \(\Q(\sqrt{13}) \) None \(2\) \(3\) \(-1\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-\beta q^{5}+(1+\beta )q^{6}+\cdots\)
8954.2.a.q 8954.a 1.a $3$ $71.498$ 3.3.404.1 None \(-3\) \(-2\) \(-7\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+(-2-\beta _{2})q^{5}+\cdots\)
8954.2.a.r 8954.a 1.a $3$ $71.498$ 3.3.229.1 None \(-3\) \(-2\) \(-1\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.s 8954.a 1.a $3$ $71.498$ 3.3.229.1 None \(3\) \(-2\) \(-1\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.t 8954.a 1.a $3$ $71.498$ 3.3.148.1 None \(3\) \(0\) \(-5\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}+(-2+\beta _{1})q^{5}+\cdots\)
8954.2.a.u 8954.a 1.a $4$ $71.498$ 4.4.11344.1 None \(-4\) \(2\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1})q^{3}+q^{4}-\beta _{2}q^{5}+(-1+\cdots)q^{6}+\cdots\)
8954.2.a.v 8954.a 1.a $4$ $71.498$ 4.4.4352.1 None \(-4\) \(4\) \(4\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.w 8954.a 1.a $4$ $71.498$ 4.4.16448.1 None \(4\) \(-2\) \(2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots\)
8954.2.a.x 8954.a 1.a $5$ $71.498$ 5.5.303952.1 None \(-5\) \(0\) \(1\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots\)
8954.2.a.y 8954.a 1.a $5$ $71.498$ 5.5.592041.1 None \(-5\) \(1\) \(6\) \(-9\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)
8954.2.a.z 8954.a 1.a $5$ $71.498$ 5.5.702521.1 None \(-5\) \(3\) \(0\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{4})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.ba 8954.a 1.a $5$ $71.498$ 5.5.303952.1 None \(5\) \(0\) \(1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{4}q^{3}+q^{4}+\beta _{1}q^{5}-\beta _{4}q^{6}+\cdots\)
8954.2.a.bb 8954.a 1.a $5$ $71.498$ 5.5.2186192.1 None \(5\) \(0\) \(6\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
8954.2.a.bc 8954.a 1.a $5$ $71.498$ 5.5.592041.1 None \(5\) \(1\) \(6\) \(9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}-\beta _{2}q^{6}+\cdots\)
8954.2.a.bd 8954.a 1.a $5$ $71.498$ 5.5.702521.1 None \(5\) \(3\) \(0\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{4})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
8954.2.a.be 8954.a 1.a $6$ $71.498$ 6.6.249645904.1 None \(-6\) \(0\) \(1\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots\)
8954.2.a.bf 8954.a 1.a $6$ $71.498$ 6.6.249645904.1 None \(6\) \(0\) \(1\) \(8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-\beta _{1}-\beta _{4})q^{5}+\cdots\)
8954.2.a.bg 8954.a 1.a $7$ $71.498$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(-1\) \(-3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}+\beta _{1}q^{6}+\cdots\)
8954.2.a.bh 8954.a 1.a $7$ $71.498$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-7\) \(1\) \(-3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{5}q^{6}+\cdots\)
8954.2.a.bi 8954.a 1.a $7$ $71.498$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(-1\) \(-3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{6}q^{5}-\beta _{1}q^{6}+\cdots\)
8954.2.a.bj 8954.a 1.a $7$ $71.498$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(7\) \(1\) \(-3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{5}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{5}q^{6}+\cdots\)
8954.2.a.bk 8954.a 1.a $12$ $71.498$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(-7\) \(-4\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{5}q^{5}+\cdots\)
8954.2.a.bl 8954.a 1.a $12$ $71.498$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(12\) \(-7\) \(-4\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+\beta _{5}q^{5}+\cdots\)
8954.2.a.bm 8954.a 1.a $14$ $71.498$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(-4\) \(-6\) \(5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)
8954.2.a.bn 8954.a 1.a $14$ $71.498$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(-10\) \(14\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{5})q^{5}+\cdots\)
8954.2.a.bo 8954.a 1.a $14$ $71.498$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(-4\) \(-6\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
8954.2.a.bp 8954.a 1.a $14$ $71.498$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(14\) \(0\) \(-10\) \(-14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(-1+\beta _{5})q^{5}+\cdots\)
8954.2.a.bq 8954.a 1.a $16$ $71.498$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(6\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{10}q^{5}+\beta _{1}q^{6}+\cdots\)
8954.2.a.br 8954.a 1.a $16$ $71.498$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(6\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{10}q^{5}-\beta _{1}q^{6}+\cdots\)
8954.2.a.bs 8954.a 1.a $22$ $71.498$ None \(-22\) \(5\) \(8\) \(-7\) $+$ $-$ $+$ $\mathrm{SU}(2)$
8954.2.a.bt 8954.a 1.a $22$ $71.498$ None \(22\) \(5\) \(8\) \(7\) $-$ $+$ $+$ $\mathrm{SU}(2)$
8954.2.a.bu 8954.a 1.a $24$ $71.498$ None \(-24\) \(8\) \(6\) \(-3\) $+$ $+$ $-$ $\mathrm{SU}(2)$
8954.2.a.bv 8954.a 1.a $24$ $71.498$ None \(24\) \(8\) \(6\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8954))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8954)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(407))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(814))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4477))\)\(^{\oplus 2}\)