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

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

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

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 5 7 23
5635.2.a.a \(1\) \(44.996\) \(\Q\) None \(-1\) \(-2\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q-q^{2}-2q^{3}-q^{4}+q^{5}+2q^{6}+3q^{8}+\cdots\)
5635.2.a.b \(1\) \(44.996\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
5635.2.a.c \(1\) \(44.996\) \(\Q\) None \(-1\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\)
5635.2.a.d \(1\) \(44.996\) \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}+2q^{3}-q^{4}-q^{5}-2q^{6}+3q^{8}+\cdots\)
5635.2.a.e \(1\) \(44.996\) \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) \(+\) \(-\) \(-\) \(q+q^{2}-2q^{3}-q^{4}-q^{5}-2q^{6}-3q^{8}+\cdots\)
5635.2.a.f \(1\) \(44.996\) \(\Q\) None \(1\) \(2\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+q^{2}+2q^{3}-q^{4}+q^{5}+2q^{6}-3q^{8}+\cdots\)
5635.2.a.g \(1\) \(44.996\) \(\Q\) None \(2\) \(-3\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}-3q^{3}+2q^{4}+q^{5}-6q^{6}+\cdots\)
5635.2.a.h \(1\) \(44.996\) \(\Q\) None \(2\) \(-2\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}-2q^{3}+2q^{4}+q^{5}-4q^{6}+\cdots\)
5635.2.a.i \(1\) \(44.996\) \(\Q\) None \(2\) \(-1\) \(-1\) \(0\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-q^{5}-2q^{6}-2q^{9}+\cdots\)
5635.2.a.j \(1\) \(44.996\) \(\Q\) None \(2\) \(0\) \(1\) \(0\) \(-\) \(-\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}-3q^{9}+2q^{10}+\cdots\)
5635.2.a.k \(1\) \(44.996\) \(\Q\) None \(2\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{9}+\cdots\)
5635.2.a.l \(1\) \(44.996\) \(\Q\) None \(2\) \(1\) \(1\) \(0\) \(-\) \(-\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+q^{5}+2q^{6}-2q^{9}+\cdots\)
5635.2.a.m \(1\) \(44.996\) \(\Q\) None \(2\) \(2\) \(-1\) \(0\) \(+\) \(+\) \(+\) \(q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots\)
5635.2.a.n \(2\) \(44.996\) \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(2\) \(0\) \(-\) \(-\) \(+\) \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+q^{5}+\cdots\)
5635.2.a.o \(2\) \(44.996\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) \(+\) \(+\) \(-\) \(q+\beta q^{2}+\beta q^{3}-q^{5}+2q^{6}-2\beta q^{8}+\cdots\)
5635.2.a.p \(2\) \(44.996\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+\beta q^{2}-\beta q^{3}+q^{5}-2q^{6}-2\beta q^{8}+\cdots\)
5635.2.a.q \(2\) \(44.996\) \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(2\) \(0\) \(-\) \(-\) \(-\) \(q+(1+\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
5635.2.a.r \(3\) \(44.996\) \(\Q(\zeta_{14})^+\) None \(-2\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q+(-1-\beta _{2})q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
5635.2.a.s \(4\) \(44.996\) 4.4.2777.1 None \(-2\) \(5\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.t \(4\) \(44.996\) 4.4.22545.1 None \(-1\) \(0\) \(4\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
5635.2.a.u \(4\) \(44.996\) 4.4.7537.1 None \(1\) \(-4\) \(4\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5635.2.a.v \(4\) \(44.996\) 4.4.15317.1 None \(2\) \(2\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.w \(4\) \(44.996\) 4.4.2777.1 None \(3\) \(-6\) \(-4\) \(0\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
5635.2.a.x \(5\) \(44.996\) 5.5.122821.1 None \(-3\) \(6\) \(-5\) \(0\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(\beta _{3}+\beta _{4})q^{4}+\cdots\)
5635.2.a.y \(5\) \(44.996\) 5.5.255877.1 None \(-1\) \(4\) \(5\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5635.2.a.z \(6\) \(44.996\) 6.6.169449536.1 None \(0\) \(0\) \(-6\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{1}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.ba \(6\) \(44.996\) 6.6.169449536.1 None \(0\) \(0\) \(6\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bb \(8\) \(44.996\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-7\) \(-8\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5635.2.a.bc \(12\) \(44.996\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(-2\) \(-12\) \(0\) \(+\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+\beta _{9}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.bd \(12\) \(44.996\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-7\) \(2\) \(12\) \(0\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{2}-\beta _{9}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5635.2.a.be \(13\) \(44.996\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-5\) \(-2\) \(13\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{10}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
5635.2.a.bf \(13\) \(44.996\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-5\) \(2\) \(-13\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{10}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
5635.2.a.bg \(13\) \(44.996\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-1\) \(-13\) \(0\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bh \(13\) \(44.996\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(1\) \(13\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bi \(15\) \(44.996\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(5\) \(0\) \(-15\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bj \(15\) \(44.996\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(5\) \(0\) \(15\) \(0\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bk \(16\) \(44.996\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(-2\) \(16\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bl \(16\) \(44.996\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-2\) \(2\) \(-16\) \(0\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bm \(17\) \(44.996\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(5\) \(-2\) \(17\) \(0\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+q^{5}+\cdots\)
5635.2.a.bn \(17\) \(44.996\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(5\) \(2\) \(-17\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots\)
5635.2.a.bo \(28\) \(44.996\) None \(-2\) \(-6\) \(-28\) \(0\) \(+\) \(+\) \(+\)
5635.2.a.bp \(28\) \(44.996\) None \(-2\) \(6\) \(28\) \(0\) \(-\) \(+\) \(+\)

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

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