Properties

Label 3626.2.a
Level $3626$
Weight $2$
Character orbit 3626.a
Rep. character $\chi_{3626}(1,\cdot)$
Character field $\Q$
Dimension $123$
Newform subspaces $35$
Sturm bound $1064$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 3626 = 2 \cdot 7^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3626.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(1064\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3626))\).

Total New Old
Modular forms 548 123 425
Cusp forms 517 123 394
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.

\(2\)\(7\)\(37\)FrickeDim
\(+\)\(+\)\(+\)$+$\(12\)
\(+\)\(+\)\(-\)$-$\(20\)
\(+\)\(-\)\(+\)$-$\(18\)
\(+\)\(-\)\(-\)$+$\(12\)
\(-\)\(+\)\(+\)$-$\(20\)
\(-\)\(+\)\(-\)$+$\(8\)
\(-\)\(-\)\(+\)$+$\(12\)
\(-\)\(-\)\(-\)$-$\(21\)
Plus space\(+\)\(44\)
Minus space\(-\)\(79\)

Trace form

\( 123 q - q^{2} - 2 q^{3} + 123 q^{4} + 6 q^{5} + 4 q^{6} - q^{8} + 133 q^{9} + O(q^{10}) \) \( 123 q - q^{2} - 2 q^{3} + 123 q^{4} + 6 q^{5} + 4 q^{6} - q^{8} + 133 q^{9} + 4 q^{10} + 6 q^{11} - 2 q^{12} - 10 q^{13} + 24 q^{15} + 123 q^{16} + 18 q^{17} + 11 q^{18} - 12 q^{19} + 6 q^{20} + 12 q^{23} + 4 q^{24} + 131 q^{25} + 4 q^{26} + 4 q^{27} + 18 q^{29} - 4 q^{31} - q^{32} + 8 q^{33} - 6 q^{34} + 133 q^{36} - q^{37} - 16 q^{38} + 44 q^{39} + 4 q^{40} - 8 q^{41} + 16 q^{43} + 6 q^{44} + 30 q^{45} + 18 q^{46} - 20 q^{47} - 2 q^{48} + q^{50} - 10 q^{52} + 54 q^{53} - 8 q^{54} + 28 q^{55} + 28 q^{57} + 12 q^{58} + 8 q^{59} + 24 q^{60} + 6 q^{61} + 14 q^{62} + 123 q^{64} + 32 q^{65} - 8 q^{66} + 14 q^{67} + 18 q^{68} + 56 q^{69} + 40 q^{71} + 11 q^{72} + 12 q^{73} - 5 q^{74} + 16 q^{75} - 12 q^{76} + 10 q^{78} + 12 q^{79} + 6 q^{80} + 195 q^{81} + 6 q^{82} + 20 q^{83} + 60 q^{85} + 4 q^{86} + 4 q^{87} + 14 q^{89} + 30 q^{90} + 12 q^{92} + 16 q^{93} + 32 q^{94} + 68 q^{95} + 4 q^{96} - 6 q^{97} - 56 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3626))\) 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 7 37
3626.2.a.a 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{13}) \) None \(-2\) \(-3\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots\)
3626.2.a.b 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{21}) \) None \(-2\) \(-2\) \(3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\)
3626.2.a.c 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{21}) \) None \(-2\) \(-1\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-q^{8}+\cdots\)
3626.2.a.d 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(-1-\beta )q^{5}+\cdots\)
3626.2.a.e 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}-\beta q^{6}+\cdots\)
3626.2.a.f 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}-\beta q^{6}+\cdots\)
3626.2.a.g 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{6}-q^{8}+5q^{9}+\cdots\)
3626.2.a.h 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-2\beta )q^{3}+q^{4}+(2-\beta )q^{5}+\cdots\)
3626.2.a.i 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{21}) \) None \(-2\) \(1\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-q^{8}+\cdots\)
3626.2.a.j 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{21}) \) None \(-2\) \(2\) \(-3\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-2+\beta )q^{5}-q^{6}+\cdots\)
3626.2.a.k 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{5}) \) None \(2\) \(-3\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta )q^{3}+q^{4}+(1-2\beta )q^{5}+\cdots\)
3626.2.a.l 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{3}) \) None \(2\) \(-2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
3626.2.a.m 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{21}) \) None \(2\) \(-1\) \(6\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta q^{3}+q^{4}+3q^{5}-\beta q^{6}+q^{8}+\cdots\)
3626.2.a.n 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}-3q^{9}+q^{16}+2\beta q^{17}+\cdots\)
3626.2.a.o 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+2\beta q^{5}+\beta q^{6}+\cdots\)
3626.2.a.p 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{6}+q^{8}-q^{9}+\cdots\)
3626.2.a.q 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{8}+\cdots\)
3626.2.a.r 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{21}) \) None \(2\) \(1\) \(-6\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-3q^{5}+\beta q^{6}+q^{8}+\cdots\)
3626.2.a.s 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{5}) \) None \(2\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+(1-3\beta )q^{5}+\beta q^{6}+\cdots\)
3626.2.a.t 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
3626.2.a.u 3626.a 1.a $2$ $28.954$ \(\Q(\sqrt{5}) \) None \(2\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(2-\beta )q^{5}+\cdots\)
3626.2.a.v 3626.a 1.a $3$ $28.954$ 3.3.733.1 None \(-3\) \(-1\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+(-1-\beta _{2})q^{5}+\cdots\)
3626.2.a.w 3626.a 1.a $3$ $28.954$ 3.3.229.1 None \(-3\) \(1\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(1+\beta _{1})q^{5}+\beta _{2}q^{6}+\cdots\)
3626.2.a.x 3626.a 1.a $4$ $28.954$ \(\Q(\sqrt{3}, \sqrt{7})\) None \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(\beta _{1}+2\beta _{3})q^{5}+\cdots\)
3626.2.a.y 3626.a 1.a $4$ $28.954$ 4.4.9792.1 None \(4\) \(-4\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{2})q^{3}+q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
3626.2.a.z 3626.a 1.a $4$ $28.954$ 4.4.2624.1 None \(4\) \(0\) \(-6\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+(-2+\cdots)q^{5}+\cdots\)
3626.2.a.ba 3626.a 1.a $4$ $28.954$ 4.4.2624.1 None \(4\) \(0\) \(6\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+(2+\cdots)q^{5}+\cdots\)
3626.2.a.bb 3626.a 1.a $4$ $28.954$ 4.4.9792.1 None \(4\) \(4\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{2})q^{3}+q^{4}-\beta _{3}q^{5}+(1+\cdots)q^{6}+\cdots\)
3626.2.a.bc 3626.a 1.a $5$ $28.954$ 5.5.2174276.1 None \(5\) \(-1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+(1+\beta _{2})q^{5}+\beta _{1}q^{6}+\cdots\)
3626.2.a.bd 3626.a 1.a $6$ $28.954$ 6.6.24635632.1 None \(-6\) \(-3\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots\)
3626.2.a.be 3626.a 1.a $6$ $28.954$ 6.6.1229312.1 None \(-6\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}-q^{8}+\cdots\)
3626.2.a.bf 3626.a 1.a $6$ $28.954$ 6.6.24635632.1 None \(-6\) \(3\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{2})q^{3}+q^{4}+(-\beta _{3}-\beta _{5})q^{5}+\cdots\)
3626.2.a.bg 3626.a 1.a $8$ $28.954$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{4}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{4}q^{6}+\cdots\)
3626.2.a.bh 3626.a 1.a $10$ $28.954$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{8}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{8}q^{6}+\cdots\)
3626.2.a.bi 3626.a 1.a $14$ $28.954$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-14\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{10}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3626))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3626)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(259))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(518))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1813))\)\(^{\oplus 2}\)