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Properties

Label 4018.2.a
Level $4018$
Weight $2$
Character orbit 4018.a
Rep. character $\chi_{4018}(1,\cdot)$
Character field $\Q$
Dimension $138$
Newform subspaces $47$
Sturm bound $1176$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4018.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 47 \)
Sturm bound: \(1176\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4018))\).

Total New Old
Modular forms 604 138 466
Cusp forms 573 138 435
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.

\(2\)\(7\)\(41\)FrickeDim
\(+\)\(+\)\(+\)$+$\(18\)
\(+\)\(+\)\(-\)$-$\(16\)
\(+\)\(-\)\(+\)$-$\(16\)
\(+\)\(-\)\(-\)$+$\(19\)
\(-\)\(+\)\(+\)$-$\(20\)
\(-\)\(+\)\(-\)$+$\(14\)
\(-\)\(-\)\(+\)$+$\(13\)
\(-\)\(-\)\(-\)$-$\(22\)
Plus space\(+\)\(64\)
Minus space\(-\)\(74\)

Trace form

\( 138 q - 2 q^{3} + 138 q^{4} + 2 q^{6} + 146 q^{9} + O(q^{10}) \) \( 138 q - 2 q^{3} + 138 q^{4} + 2 q^{6} + 146 q^{9} + 4 q^{10} + 10 q^{11} - 2 q^{12} + 10 q^{13} + 12 q^{15} + 138 q^{16} + 8 q^{17} + 16 q^{18} + 14 q^{19} + 6 q^{22} + 2 q^{24} + 142 q^{25} + 10 q^{26} + 4 q^{27} + 2 q^{29} + 4 q^{30} - 8 q^{31} - 8 q^{33} - 4 q^{34} + 146 q^{36} - 60 q^{37} + 2 q^{38} - 8 q^{39} + 4 q^{40} + 4 q^{41} - 16 q^{43} + 10 q^{44} - 24 q^{45} - 8 q^{46} - 16 q^{47} - 2 q^{48} + 24 q^{50} + 4 q^{51} + 10 q^{52} - 10 q^{53} - 4 q^{54} - 4 q^{55} - 56 q^{57} + 10 q^{58} - 4 q^{59} + 12 q^{60} + 8 q^{61} + 138 q^{64} - 28 q^{65} - 8 q^{66} - 46 q^{67} + 8 q^{68} - 16 q^{69} - 4 q^{71} + 16 q^{72} + 40 q^{73} - 6 q^{75} + 14 q^{76} + 186 q^{81} + 2 q^{82} - 16 q^{83} + 72 q^{85} + 48 q^{87} + 6 q^{88} - 60 q^{89} + 44 q^{90} - 40 q^{93} + 76 q^{95} + 2 q^{96} + 16 q^{97} + 66 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\) 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 41
4018.2.a.a 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(-3\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}-q^{5}+3q^{6}-q^{8}+\cdots\)
4018.2.a.b 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(-3\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}+q^{4}+q^{5}+3q^{6}-q^{8}+\cdots\)
4018.2.a.c 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(-2\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}-2q^{5}+2q^{6}-q^{8}+\cdots\)
4018.2.a.d 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(-2\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+2q^{5}+2q^{6}-q^{8}+\cdots\)
4018.2.a.e 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
4018.2.a.f 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(-1\) \(3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-q^{8}+\cdots\)
4018.2.a.g 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
4018.2.a.h 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
4018.2.a.i 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(2\) \(-4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-4q^{5}-2q^{6}-q^{8}+\cdots\)
4018.2.a.j 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(2\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}+2q^{5}-2q^{6}-q^{8}+\cdots\)
4018.2.a.k 4018.a 1.a $1$ $32.084$ \(\Q\) None \(-1\) \(3\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}+q^{4}+q^{5}-3q^{6}-q^{8}+\cdots\)
4018.2.a.l 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(-2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+2q^{5}-2q^{6}+q^{8}+\cdots\)
4018.2.a.m 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(-1\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-3q^{5}-q^{6}+q^{8}+\cdots\)
4018.2.a.n 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+q^{8}-3q^{9}+4q^{10}+\cdots\)
4018.2.a.o 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
4018.2.a.p 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(1\) \(1\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+q^{8}+\cdots\)
4018.2.a.q 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}+q^{8}+\cdots\)
4018.2.a.r 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(2\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-2q^{5}+2q^{6}+q^{8}+\cdots\)
4018.2.a.s 4018.a 1.a $1$ $32.084$ \(\Q\) None \(1\) \(3\) \(1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}+q^{5}+3q^{6}+q^{8}+\cdots\)
4018.2.a.t 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{5}) \) None \(-2\) \(-2\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{8}+\cdots\)
4018.2.a.u 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{33}) \) None \(-2\) \(-1\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{5}+\beta q^{6}-q^{8}+\cdots\)
4018.2.a.v 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{33}) \) None \(-2\) \(1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-\beta q^{5}-\beta q^{6}-q^{8}+\cdots\)
4018.2.a.w 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{5}) \) None \(-2\) \(2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots\)
4018.2.a.x 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{3}) \) None \(2\) \(-4\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}+(-1-\beta )q^{5}-2q^{6}+\cdots\)
4018.2.a.y 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+2\beta )q^{5}+\cdots\)
4018.2.a.z 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
4018.2.a.ba 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-2\beta q^{5}+\beta q^{6}+\cdots\)
4018.2.a.bb 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(1+\beta )q^{6}+\cdots\)
4018.2.a.bc 4018.a 1.a $2$ $32.084$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta )q^{3}+q^{4}+(1+2\beta )q^{5}+\cdots\)
4018.2.a.bd 4018.a 1.a $3$ $32.084$ 3.3.404.1 None \(-3\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}-\beta _{2})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4018.2.a.be 4018.a 1.a $3$ $32.084$ 3.3.404.1 None \(-3\) \(0\) \(2\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-\beta _{1}+\beta _{2})q^{3}+q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
4018.2.a.bf 4018.a 1.a $3$ $32.084$ 3.3.321.1 None \(3\) \(-3\) \(4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{2})q^{5}-q^{6}+\cdots\)
4018.2.a.bg 4018.a 1.a $3$ $32.084$ 3.3.568.1 None \(3\) \(-1\) \(-1\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots\)
4018.2.a.bh 4018.a 1.a $3$ $32.084$ 3.3.321.1 None \(3\) \(3\) \(-4\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1+\beta _{2})q^{5}+q^{6}+\cdots\)
4018.2.a.bi 4018.a 1.a $4$ $32.084$ 4.4.113481.1 None \(-4\) \(-4\) \(-3\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+(-1+\beta _{3})q^{5}+q^{6}+\cdots\)
4018.2.a.bj 4018.a 1.a $4$ $32.084$ 4.4.11348.1 None \(-4\) \(1\) \(-3\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
4018.2.a.bk 4018.a 1.a $4$ $32.084$ 4.4.113481.1 None \(-4\) \(4\) \(3\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(1-\beta _{3})q^{5}-q^{6}+\cdots\)
4018.2.a.bl 4018.a 1.a $4$ $32.084$ 4.4.37108.1 None \(4\) \(-3\) \(-3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
4018.2.a.bm 4018.a 1.a $4$ $32.084$ 4.4.37108.1 None \(4\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2})q^{3}+q^{4}+(1-\beta _{1})q^{5}+\cdots\)
4018.2.a.bn 4018.a 1.a $6$ $32.084$ 6.6.52046292.1 None \(-6\) \(-1\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+\beta _{4}q^{5}-\beta _{3}q^{6}+\cdots\)
4018.2.a.bo 4018.a 1.a $6$ $32.084$ 6.6.52046292.1 None \(-6\) \(1\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}-\beta _{4}q^{5}+\beta _{3}q^{6}+\cdots\)
4018.2.a.bp 4018.a 1.a $6$ $32.084$ 6.6.5163008.1 None \(6\) \(-4\) \(-12\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{4})q^{3}+q^{4}+\cdots\)
4018.2.a.bq 4018.a 1.a $6$ $32.084$ 6.6.5163008.1 None \(6\) \(4\) \(12\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{2}+\beta _{3}-\beta _{4})q^{3}+q^{4}+\cdots\)
4018.2.a.br 4018.a 1.a $10$ $32.084$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(-4\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots\)
4018.2.a.bs 4018.a 1.a $10$ $32.084$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-10\) \(4\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+\beta _{3}q^{6}+\cdots\)
4018.2.a.bt 4018.a 1.a $10$ $32.084$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-1\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{4}q^{5}-\beta _{1}q^{6}+\cdots\)
4018.2.a.bu 4018.a 1.a $10$ $32.084$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(1\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{4}q^{5}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2009))\)\(^{\oplus 2}\)