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Properties

Label 5635.2.a
Level $5635$
Weight $2$
Character orbit 5635.a
Rep. character $\chi_{5635}(1,\cdot)$
Character field $\Q$
Dimension $302$
Newform subspaces $42$
Sturm bound $1344$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5635 = 5 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5635.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 42 \)
Sturm bound: \(1344\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5635))\).

Total New Old
Modular forms 688 302 386
Cusp forms 657 302 355
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.

\(5\)\(7\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(41\)
\(+\)\(+\)\(-\)$-$\(33\)
\(+\)\(-\)\(+\)$-$\(37\)
\(+\)\(-\)\(-\)$+$\(40\)
\(-\)\(+\)\(+\)$-$\(45\)
\(-\)\(+\)\(-\)$+$\(29\)
\(-\)\(-\)\(+\)$+$\(31\)
\(-\)\(-\)\(-\)$-$\(46\)
Plus space\(+\)\(141\)
Minus space\(-\)\(161\)

Trace form

\( 302 q - 2 q^{2} + 306 q^{4} - 10 q^{6} - 12 q^{8} + 298 q^{9} + O(q^{10}) \) \( 302 q - 2 q^{2} + 306 q^{4} - 10 q^{6} - 12 q^{8} + 298 q^{9} + 14 q^{12} + 24 q^{13} + 4 q^{15} + 322 q^{16} - 4 q^{17} + 4 q^{18} + 8 q^{20} + 20 q^{22} - 6 q^{23} + 4 q^{24} + 302 q^{25} - 14 q^{26} - 12 q^{27} + 14 q^{29} - 16 q^{30} + 18 q^{31} - 26 q^{32} - 48 q^{33} + 288 q^{36} - 36 q^{37} - 16 q^{38} - 32 q^{39} - 30 q^{41} - 48 q^{43} + 20 q^{44} + 24 q^{47} + 66 q^{48} - 2 q^{50} + 44 q^{51} + 54 q^{52} + 28 q^{53} + 42 q^{54} + 8 q^{55} - 56 q^{57} + 6 q^{58} + 2 q^{59} + 44 q^{60} + 44 q^{61} + 62 q^{62} + 376 q^{64} + 4 q^{65} + 60 q^{66} - 36 q^{67} + 44 q^{68} + 70 q^{71} + 24 q^{72} + 12 q^{73} + 24 q^{74} + 16 q^{76} + 34 q^{78} - 20 q^{79} + 286 q^{81} - 62 q^{82} + 36 q^{83} + 10 q^{85} + 116 q^{86} - 16 q^{87} - 24 q^{88} - 4 q^{89} + 36 q^{90} - 12 q^{92} - 52 q^{93} - 10 q^{94} - 8 q^{95} + 6 q^{96} + 8 q^{97} - 152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5635))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 23
5635.2.a.a 5635.a 1.a $1$ $44.996$ \(\Q\) None \(-1\) \(-2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+3q^{8}+\cdots\)
5635.2.a.b 5635.a 1.a $1$ $44.996$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
5635.2.a.c 5635.a 1.a $1$ $44.996$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
5635.2.a.d 5635.a 1.a $1$ $44.996$ \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-q^{5}-2q^{6}+3q^{8}+\cdots\)
5635.2.a.e 5635.a 1.a $1$ $44.996$ \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-3q^{8}+\cdots\)
5635.2.a.f 5635.a 1.a $1$ $44.996$ \(\Q\) None \(1\) \(2\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+q^{5}+2q^{6}-3q^{8}+\cdots\)
5635.2.a.g 5635.a 1.a $1$ $44.996$ \(\Q\) None \(2\) \(-3\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+2q^{4}+q^{5}-6q^{6}+\cdots\)
5635.2.a.h 5635.a 1.a $1$ $44.996$ \(\Q\) None \(2\) \(-2\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
5635.2.a.i 5635.a 1.a $1$ $44.996$ \(\Q\) None \(2\) \(-1\) \(-1\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{9}+\cdots\)
5635.2.a.j 5635.a 1.a $1$ $44.996$ \(\Q\) None \(2\) \(0\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{5}-3q^{9}+2q^{10}+\cdots\)
5635.2.a.k 5635.a 1.a $1$ $44.996$ \(\Q\) None \(2\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{9}+\cdots\)
5635.2.a.l 5635.a 1.a $1$ $44.996$ \(\Q\) None \(2\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{9}+\cdots\)
5635.2.a.m 5635.a 1.a $1$ $44.996$ \(\Q\) None \(2\) \(2\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
5635.2.a.n 5635.a 1.a $2$ $44.996$ \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+q^{5}+\cdots\)
5635.2.a.o 5635.a 1.a $2$ $44.996$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}-q^{5}+2q^{6}-2\beta q^{8}+\cdots\)
5635.2.a.p 5635.a 1.a $2$ $44.996$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
5635.2.a.q 5635.a 1.a $2$ $44.996$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
5635.2.a.r 5635.a 1.a $3$ $44.996$ \(\Q(\zeta_{14})^+\) None \(-2\) \(0\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
5635.2.a.s 5635.a 1.a $4$ $44.996$ 4.4.2777.1 None \(-2\) \(5\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.t 5635.a 1.a $4$ $44.996$ 4.4.22545.1 None \(-1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
5635.2.a.u 5635.a 1.a $4$ $44.996$ 4.4.7537.1 None \(1\) \(-4\) \(4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5635.2.a.v 5635.a 1.a $4$ $44.996$ 4.4.15317.1 None \(2\) \(2\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.w 5635.a 1.a $4$ $44.996$ 4.4.2777.1 None \(3\) \(-6\) \(-4\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
5635.2.a.x 5635.a 1.a $5$ $44.996$ 5.5.122821.1 None \(-3\) \(6\) \(-5\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(\beta _{3}+\beta _{4})q^{4}+\cdots\)
5635.2.a.y 5635.a 1.a $5$ $44.996$ 5.5.255877.1 None \(-1\) \(4\) \(5\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5635.2.a.z 5635.a 1.a $6$ $44.996$ 6.6.169449536.1 None \(0\) \(0\) \(-6\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.ba 5635.a 1.a $6$ $44.996$ 6.6.169449536.1 None \(0\) \(0\) \(6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bb 5635.a 1.a $8$ $44.996$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-7\) \(-8\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5635.2.a.bc 5635.a 1.a $12$ $44.996$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(-2\) \(-12\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{9}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.bd 5635.a 1.a $12$ $44.996$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(2\) \(12\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{9}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.be 5635.a 1.a $13$ $44.996$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-5\) \(-2\) \(13\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
5635.2.a.bf 5635.a 1.a $13$ $44.996$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-5\) \(2\) \(-13\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
5635.2.a.bg 5635.a 1.a $13$ $44.996$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-1\) \(-13\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bh 5635.a 1.a $13$ $44.996$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(1\) \(13\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bi 5635.a 1.a $15$ $44.996$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(5\) \(0\) \(-15\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bj 5635.a 1.a $15$ $44.996$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(5\) \(0\) \(15\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bk 5635.a 1.a $16$ $44.996$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(-2\) \(16\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bl 5635.a 1.a $16$ $44.996$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(2\) \(-16\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bm 5635.a 1.a $17$ $44.996$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(5\) \(-2\) \(17\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bn 5635.a 1.a $17$ $44.996$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(5\) \(2\) \(-17\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bo 5635.a 1.a $28$ $44.996$ None \(-2\) \(-6\) \(-28\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$
5635.2.a.bp 5635.a 1.a $28$ $44.996$ None \(-2\) \(6\) \(28\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5635))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5635)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 2}\)