Properties

Label 3042.2.a
Level $3042$
Weight $2$
Character orbit 3042.a
Rep. character $\chi_{3042}(1,\cdot)$
Character field $\Q$
Dimension $65$
Newform subspaces $35$
Sturm bound $1092$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3042 = 2 \cdot 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3042.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(1092\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3042))\).

Total New Old
Modular forms 602 65 537
Cusp forms 491 65 426
Eisenstein series 111 0 111

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

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(8\)
\(+\)\(+\)\(-\)\(-\)\(5\)
\(+\)\(-\)\(+\)\(-\)\(11\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(8\)
\(-\)\(+\)\(-\)\(+\)\(5\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(12\)
Plus space\(+\)\(29\)
Minus space\(-\)\(36\)

Trace form

\( 65 q - q^{2} + 65 q^{4} - 2 q^{5} - q^{8} + O(q^{10}) \) \( 65 q - q^{2} + 65 q^{4} - 2 q^{5} - q^{8} - 4 q^{10} - 4 q^{14} + 65 q^{16} - 6 q^{17} + 12 q^{19} - 2 q^{20} - 6 q^{22} - 8 q^{23} + 69 q^{25} + 8 q^{29} + 8 q^{31} - q^{32} + 2 q^{34} + 12 q^{35} - 6 q^{37} + 10 q^{38} - 4 q^{40} - 10 q^{41} + 14 q^{43} + 12 q^{46} + 24 q^{47} + 85 q^{49} - 7 q^{50} - 4 q^{53} + 16 q^{55} - 4 q^{56} - 6 q^{58} - 12 q^{59} - 12 q^{61} + 16 q^{62} + 65 q^{64} + 8 q^{67} - 6 q^{68} + 20 q^{70} - 16 q^{71} - 22 q^{73} + 20 q^{74} + 12 q^{76} - 12 q^{77} + 4 q^{79} - 2 q^{80} + 6 q^{82} + 24 q^{83} - 16 q^{85} - 8 q^{86} - 6 q^{88} + 14 q^{89} - 8 q^{92} + 16 q^{94} - 20 q^{95} + 6 q^{97} - 9 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3042))\) 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 13
3042.2.a.a 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(-3\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}+q^{7}-q^{8}+3q^{10}+\cdots\)
3042.2.a.b 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(-2\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots\)
3042.2.a.c 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(-2\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}+2q^{7}-q^{8}+2q^{10}+\cdots\)
3042.2.a.d 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
3042.2.a.e 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
3042.2.a.f 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-4q^{7}-q^{8}-2q^{10}+\cdots\)
3042.2.a.g 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(3\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-3q^{7}-q^{8}-3q^{10}+\cdots\)
3042.2.a.h 3042.a 1.a $1$ $24.290$ \(\Q\) None \(-1\) \(0\) \(3\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-2q^{7}-q^{8}-3q^{10}+\cdots\)
3042.2.a.i 3042.a 1.a $1$ $24.290$ \(\Q\) None \(1\) \(0\) \(-3\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+2q^{7}+q^{8}-3q^{10}+\cdots\)
3042.2.a.j 3042.a 1.a $1$ $24.290$ \(\Q\) None \(1\) \(0\) \(-3\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+3q^{7}+q^{8}-3q^{10}+\cdots\)
3042.2.a.k 3042.a 1.a $1$ $24.290$ \(\Q\) None \(1\) \(0\) \(-1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
3042.2.a.l 3042.a 1.a $1$ $24.290$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}-q^{7}+q^{8}-q^{10}+\cdots\)
3042.2.a.m 3042.a 1.a $1$ $24.290$ \(\Q\) None \(1\) \(0\) \(1\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-2q^{7}+q^{8}+q^{10}+\cdots\)
3042.2.a.n 3042.a 1.a $1$ $24.290$ \(\Q\) None \(1\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}-2q^{7}+q^{8}+2q^{10}+\cdots\)
3042.2.a.o 3042.a 1.a $1$ $24.290$ \(\Q\) None \(1\) \(0\) \(2\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+2q^{7}+q^{8}+2q^{10}+\cdots\)
3042.2.a.p 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(-4\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-2+\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
3042.2.a.q 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta )q^{5}+\beta q^{7}-q^{8}+\cdots\)
3042.2.a.r 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{10}) \) None \(-2\) \(0\) \(-2\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta )q^{5}-\beta q^{7}-q^{8}+\cdots\)
3042.2.a.s 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(0\) \(-6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}+(-3+\beta )q^{7}-q^{8}+\cdots\)
3042.2.a.t 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{3}) \) None \(-2\) \(0\) \(6\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+q^{16}+\cdots\)
3042.2.a.u 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-6\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}+q^{16}+\cdots\)
3042.2.a.v 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(0\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+(3+\beta )q^{7}+q^{8}+\cdots\)
3042.2.a.w 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}+\beta q^{7}+q^{8}+\cdots\)
3042.2.a.x 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{10}) \) None \(2\) \(0\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta )q^{5}-\beta q^{7}+q^{8}+\cdots\)
3042.2.a.y 3042.a 1.a $2$ $24.290$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(4\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(2+\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
3042.2.a.z 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(-2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2\beta _{1}q^{5}+(-2\beta _{1}+2\beta _{2})q^{7}+\cdots\)
3042.2.a.ba 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(-1\) \(9\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1-3\beta _{1}+\beta _{2})q^{5}+(4+\cdots)q^{7}+\cdots\)
3042.2.a.bb 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
3042.2.a.bc 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(1\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}+(2\beta _{1}+\beta _{2})q^{7}+\cdots\)
3042.2.a.bd 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(-3\) \(0\) \(3\) \(3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
3042.2.a.be 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
3042.2.a.bf 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(-2\beta _{1}-\beta _{2})q^{7}+\cdots\)
3042.2.a.bg 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(-1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta _{1}q^{5}+(2\beta _{1}+\beta _{2})q^{7}+\cdots\)
3042.2.a.bh 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(1\) \(-9\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-\beta _{1}-2\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
3042.2.a.bi 3042.a 1.a $3$ $24.290$ \(\Q(\zeta_{14})^+\) None \(3\) \(0\) \(2\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2\beta _{1}q^{5}+(2\beta _{1}-2\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3042))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(338))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1014))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1521))\)\(^{\oplus 2}\)