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Properties

Label 4655.2.a
Level $4655$
Weight $2$
Character orbit 4655.a
Rep. character $\chi_{4655}(1,\cdot)$
Character field $\Q$
Dimension $246$
Newform subspaces $45$
Sturm bound $1120$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4655 = 5 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4655.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(1120\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(11\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4655))\).

Total New Old
Modular forms 576 246 330
Cusp forms 545 246 299
Eisenstein series 31 0 31

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

\(5\)\(7\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(23\)
\(+\)\(+\)\(-\)\(-\)\(39\)
\(+\)\(-\)\(+\)\(-\)\(36\)
\(+\)\(-\)\(-\)\(+\)\(24\)
\(-\)\(+\)\(+\)\(-\)\(37\)
\(-\)\(+\)\(-\)\(+\)\(21\)
\(-\)\(-\)\(+\)\(+\)\(27\)
\(-\)\(-\)\(-\)\(-\)\(39\)
Plus space\(+\)\(95\)
Minus space\(-\)\(151\)

Trace form

\( 246 q + 4 q^{2} + 250 q^{4} + 2 q^{5} - 8 q^{6} + 254 q^{9} + O(q^{10}) \) \( 246 q + 4 q^{2} + 250 q^{4} + 2 q^{5} - 8 q^{6} + 254 q^{9} + 8 q^{11} + 8 q^{12} - 4 q^{13} + 4 q^{15} + 282 q^{16} + 4 q^{17} + 44 q^{18} + 14 q^{20} + 48 q^{22} + 4 q^{23} + 24 q^{24} + 246 q^{25} + 4 q^{26} - 12 q^{27} + 36 q^{29} - 8 q^{30} - 16 q^{31} + 24 q^{32} + 20 q^{33} + 24 q^{34} + 274 q^{36} + 8 q^{37} + 6 q^{38} + 12 q^{41} + 4 q^{43} + 24 q^{44} + 18 q^{45} + 44 q^{46} + 20 q^{47} + 4 q^{48} + 4 q^{50} + 88 q^{51} - 28 q^{52} + 32 q^{53} + 32 q^{54} + 8 q^{55} - 4 q^{57} - 8 q^{58} - 24 q^{59} + 44 q^{60} - 4 q^{61} - 16 q^{62} + 298 q^{64} + 44 q^{67} - 36 q^{68} + 64 q^{69} + 80 q^{71} + 36 q^{72} - 4 q^{73} + 44 q^{74} + 40 q^{78} + 24 q^{79} + 22 q^{80} + 342 q^{81} + 16 q^{82} + 68 q^{83} + 12 q^{85} - 132 q^{86} + 48 q^{87} + 28 q^{88} + 20 q^{89} - 84 q^{92} + 44 q^{94} - 8 q^{95} + 8 q^{96} - 48 q^{97} + 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4655))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 19
4655.2.a.a 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.a.b \(-2\) \(-3\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+2q^{4}-q^{5}+6q^{6}+\cdots\)
4655.2.a.b 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.f \(-2\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}-3q^{9}+2q^{10}+\cdots\)
4655.2.a.c 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.e \(-2\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}-3q^{9}+2q^{10}+\cdots\)
4655.2.a.d 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.f \(-2\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-3q^{9}-2q^{10}+\cdots\)
4655.2.a.e 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.e \(-2\) \(0\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}-3q^{9}-2q^{10}+\cdots\)
4655.2.a.f 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.a.a \(-2\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{9}+\cdots\)
4655.2.a.g 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.d \(-1\) \(-1\) \(1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{5}+q^{6}+3q^{8}+\cdots\)
4655.2.a.h 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.d \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}+3q^{8}+\cdots\)
4655.2.a.i 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.a.c \(-1\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}+q^{5}-q^{6}+3q^{8}+\cdots\)
4655.2.a.j 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.c \(0\) \(-2\) \(-1\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}-q^{5}+q^{9}-3q^{11}+\cdots\)
4655.2.a.k 4655.a 1.a $1$ $37.170$ \(\Q\) None 4655.2.a.k \(0\) \(-1\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}-2q^{9}-3q^{11}+\cdots\)
4655.2.a.l 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.b \(0\) \(0\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{5}-3q^{9}+q^{11}+2q^{13}+\cdots\)
4655.2.a.m 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.b \(0\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-3q^{9}+q^{11}-2q^{13}+\cdots\)
4655.2.a.n 4655.a 1.a $1$ $37.170$ \(\Q\) None 4655.2.a.k \(0\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}-2q^{9}-3q^{11}+\cdots\)
4655.2.a.o 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.c \(0\) \(2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}+q^{5}+q^{9}-3q^{11}+\cdots\)
4655.2.a.p 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.a.e \(1\) \(0\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-3q^{8}-3q^{9}-q^{10}+\cdots\)
4655.2.a.q 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.a.d \(1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
4655.2.a.r 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.a \(2\) \(-2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
4655.2.a.s 4655.a 1.a $1$ $37.170$ \(\Q\) None 665.2.j.a \(2\) \(2\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
4655.2.a.t 4655.a 1.a $2$ $37.170$ \(\Q(\sqrt{17}) \) None 665.2.a.f \(-2\) \(1\) \(-2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta )q^{3}-q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
4655.2.a.u 4655.a 1.a $3$ $37.170$ 3.3.148.1 None 95.2.a.a \(1\) \(-2\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
4655.2.a.v 4655.a 1.a $3$ $37.170$ 3.3.148.1 None 665.2.a.g \(1\) \(-1\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
4655.2.a.w 4655.a 1.a $3$ $37.170$ 3.3.229.1 None 665.2.j.g \(1\) \(-1\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+\beta _{2}q^{3}+(2-\beta _{1})q^{4}-q^{5}+\cdots\)
4655.2.a.x 4655.a 1.a $3$ $37.170$ 3.3.229.1 None 665.2.j.g \(1\) \(1\) \(3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-\beta _{2}q^{3}+(2-\beta _{1})q^{4}+q^{5}+\cdots\)
4655.2.a.y 4655.a 1.a $4$ $37.170$ 4.4.11344.1 None 95.2.a.b \(-2\) \(-2\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{3}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
4655.2.a.z 4655.a 1.a $4$ $37.170$ 4.4.6224.1 None 4655.2.a.z \(0\) \(-2\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
4655.2.a.ba 4655.a 1.a $4$ $37.170$ 4.4.6224.1 None 4655.2.a.z \(0\) \(2\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
4655.2.a.bb 4655.a 1.a $4$ $37.170$ 4.4.11348.1 None 665.2.a.h \(1\) \(-2\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
4655.2.a.bc 4655.a 1.a $6$ $37.170$ 6.6.79799552.1 None 665.2.a.i \(-1\) \(4\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4655.2.a.bd 4655.a 1.a $7$ $37.170$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 665.2.a.j \(3\) \(-1\) \(7\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)
4655.2.a.be 4655.a 1.a $8$ $37.170$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 665.2.j.i \(1\) \(-4\) \(8\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
4655.2.a.bf 4655.a 1.a $8$ $37.170$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 665.2.j.h \(1\) \(-2\) \(-8\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
4655.2.a.bg 4655.a 1.a $8$ $37.170$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 665.2.j.h \(1\) \(2\) \(8\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
4655.2.a.bh 4655.a 1.a $8$ $37.170$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 665.2.j.i \(1\) \(4\) \(-8\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}+\beta _{5}+\beta _{7})q^{3}+\cdots\)
4655.2.a.bi 4655.a 1.a $8$ $37.170$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 665.2.a.k \(2\) \(3\) \(-8\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{4}+\cdots\)
4655.2.a.bj 4655.a 1.a $10$ $37.170$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 4655.2.a.bj \(0\) \(-2\) \(10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4655.2.a.bk 4655.a 1.a $10$ $37.170$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 4655.2.a.bj \(0\) \(2\) \(-10\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+\beta _{2}q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
4655.2.a.bl 4655.a 1.a $11$ $37.170$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 665.2.j.j \(0\) \(-5\) \(-11\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4655.2.a.bm 4655.a 1.a $11$ $37.170$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None 665.2.j.j \(0\) \(5\) \(11\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4655.2.a.bn 4655.a 1.a $12$ $37.170$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 665.2.j.k \(-4\) \(-7\) \(12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4655.2.a.bo 4655.a 1.a $12$ $37.170$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 665.2.j.k \(-4\) \(7\) \(-12\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{9})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4655.2.a.bp 4655.a 1.a $13$ $37.170$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 4655.2.a.bp \(2\) \(-3\) \(-13\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
4655.2.a.bq 4655.a 1.a $13$ $37.170$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 4655.2.a.bp \(2\) \(3\) \(13\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
4655.2.a.br 4655.a 1.a $26$ $37.170$ None 4655.2.a.br \(4\) \(-6\) \(-26\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$
4655.2.a.bs 4655.a 1.a $26$ $37.170$ None 4655.2.a.br \(4\) \(6\) \(26\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4655))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4655)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(665))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(931))\)\(^{\oplus 2}\)