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Properties

Label 3018.2.a
Level $3018$
Weight $2$
Character orbit 3018.a
Rep. character $\chi_{3018}(1,\cdot)$
Character field $\Q$
Dimension $85$
Newform subspaces $13$
Sturm bound $1008$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 3018 = 2 \cdot 3 \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3018.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(1008\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3018))\).

Total New Old
Modular forms 508 85 423
Cusp forms 501 85 416
Eisenstein series 7 0 7

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

\(2\)\(3\)\(503\)FrickeDim
\(+\)\(+\)\(+\)$+$\(14\)
\(+\)\(+\)\(-\)$-$\(7\)
\(+\)\(-\)\(+\)$-$\(12\)
\(+\)\(-\)\(-\)$+$\(9\)
\(-\)\(+\)\(+\)$-$\(12\)
\(-\)\(+\)\(-\)$+$\(9\)
\(-\)\(-\)\(+\)$+$\(5\)
\(-\)\(-\)\(-\)$-$\(17\)
Plus space\(+\)\(37\)
Minus space\(-\)\(48\)

Trace form

\( 85 q + q^{2} + q^{3} + 85 q^{4} - 2 q^{5} + q^{6} + q^{8} + 85 q^{9} + O(q^{10}) \) \( 85 q + q^{2} + q^{3} + 85 q^{4} - 2 q^{5} + q^{6} + q^{8} + 85 q^{9} + 2 q^{10} - 4 q^{11} + q^{12} + 6 q^{13} - 2 q^{15} + 85 q^{16} + 10 q^{17} + q^{18} - 2 q^{20} + 8 q^{21} + 12 q^{22} + 16 q^{23} + q^{24} + 99 q^{25} + 6 q^{26} + q^{27} + 14 q^{29} + 2 q^{30} + q^{32} - 4 q^{33} + 2 q^{34} - 32 q^{35} + 85 q^{36} + 2 q^{37} - 4 q^{38} + 6 q^{39} + 2 q^{40} - 22 q^{41} + 8 q^{42} - 4 q^{43} - 4 q^{44} - 2 q^{45} - 8 q^{47} + q^{48} + 77 q^{49} + 15 q^{50} - 10 q^{51} + 6 q^{52} - 2 q^{53} + q^{54} - 32 q^{55} + 16 q^{57} + 18 q^{58} - 44 q^{59} - 2 q^{60} - 2 q^{61} + 16 q^{62} + 85 q^{64} - 20 q^{65} - 4 q^{66} - 4 q^{67} + 10 q^{68} - 8 q^{69} + 24 q^{70} - 16 q^{71} + q^{72} + 10 q^{73} + 6 q^{74} + 31 q^{75} - 16 q^{77} + 14 q^{78} - 8 q^{79} - 2 q^{80} + 85 q^{81} + 26 q^{82} - 44 q^{83} + 8 q^{84} + 12 q^{85} + 4 q^{86} + 6 q^{87} + 12 q^{88} + 2 q^{89} + 2 q^{90} + 40 q^{91} + 16 q^{92} + 20 q^{93} + 16 q^{94} + 16 q^{95} + q^{96} + 50 q^{97} + 25 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3018))\) 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 3 503
3018.2.a.a 3018.a 1.a $1$ $24.099$ \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
3018.2.a.b 3018.a 1.a $1$ $24.099$ \(\Q\) None \(-1\) \(-1\) \(3\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}-5q^{7}+\cdots\)
3018.2.a.c 3018.a 1.a $1$ $24.099$ \(\Q\) None \(1\) \(-1\) \(-1\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3q^{7}+\cdots\)
3018.2.a.d 3018.a 1.a $1$ $24.099$ \(\Q\) None \(1\) \(-1\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots\)
3018.2.a.e 3018.a 1.a $1$ $24.099$ \(\Q\) None \(1\) \(1\) \(-3\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots\)
3018.2.a.f 3018.a 1.a $4$ $24.099$ 4.4.1957.1 None \(4\) \(4\) \(-4\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
3018.2.a.g 3018.a 1.a $6$ $24.099$ 6.6.28406549.1 None \(-6\) \(-6\) \(1\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{2}q^{5}+q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
3018.2.a.h 3018.a 1.a $9$ $24.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-9\) \(9\) \(1\) \(-11\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
3018.2.a.i 3018.a 1.a $9$ $24.099$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(9\) \(-9\) \(-7\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta _{4})q^{5}-q^{6}+\cdots\)
3018.2.a.j 3018.a 1.a $10$ $24.099$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(-10\) \(6\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(1-\beta _{3})q^{5}-q^{6}+\cdots\)
3018.2.a.k 3018.a 1.a $12$ $24.099$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(12\) \(-3\) \(11\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+(1+\cdots)q^{7}+\cdots\)
3018.2.a.l 3018.a 1.a $13$ $24.099$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-13\) \(-13\) \(-4\) \(6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-\beta _{7}q^{7}+\cdots\)
3018.2.a.m 3018.a 1.a $17$ $24.099$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(17\) \(17\) \(7\) \(13\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3018))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3018)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1509))\)\(^{\oplus 2}\)