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Properties

Label 1512.2.a
Level $1512$
Weight $2$
Character orbit 1512.a
Rep. character $\chi_{1512}(1,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $18$
Sturm bound $576$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1512.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 18 \)
Sturm bound: \(576\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1512))\).

Total New Old
Modular forms 312 24 288
Cusp forms 265 24 241
Eisenstein series 47 0 47

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

\(2\)\(3\)\(7\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(-\)\(+\)$-$\(4\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(3\)
\(-\)\(+\)\(-\)$+$\(3\)
\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)$-$\(3\)
Plus space\(+\)\(10\)
Minus space\(-\)\(14\)

Trace form

\( 24 q + O(q^{10}) \) \( 24 q - 16 q^{13} + 12 q^{25} + 8 q^{31} + 52 q^{37} + 4 q^{43} + 24 q^{49} - 16 q^{55} + 56 q^{61} - 20 q^{67} - 8 q^{73} + 16 q^{79} + 24 q^{85} + 4 q^{91} - 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1512))\) 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 7
1512.2.a.a 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(-4\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{5}-q^{7}-4q^{11}-q^{13}-3q^{17}+\cdots\)
1512.2.a.b 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-6q^{11}+4q^{13}+3q^{17}+\cdots\)
1512.2.a.c 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-q^{11}-4q^{13}+6q^{17}+\cdots\)
1512.2.a.d 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(-1\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}+2q^{11}-4q^{13}+3q^{17}+\cdots\)
1512.2.a.e 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-3q^{11}-2q^{17}+q^{19}+\cdots\)
1512.2.a.f 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(-1\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+q^{7}-6q^{13}+7q^{17}-8q^{19}+\cdots\)
1512.2.a.g 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}-2q^{11}-4q^{13}-3q^{17}+\cdots\)
1512.2.a.h 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+q^{11}-4q^{13}-6q^{17}+\cdots\)
1512.2.a.i 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{5}-q^{7}+6q^{11}+4q^{13}-3q^{17}+\cdots\)
1512.2.a.j 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}-6q^{13}-7q^{17}-8q^{19}+\cdots\)
1512.2.a.k 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{5}+q^{7}+3q^{11}+2q^{17}+q^{19}+\cdots\)
1512.2.a.l 1512.a 1.a $1$ $12.073$ \(\Q\) None \(0\) \(0\) \(4\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{5}-q^{7}+4q^{11}-q^{13}+3q^{17}+\cdots\)
1512.2.a.m 1512.a 1.a $2$ $12.073$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(-4\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2+\beta )q^{5}+q^{7}-3\beta q^{11}+2\beta q^{13}+\cdots\)
1512.2.a.n 1512.a 1.a $2$ $12.073$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(-1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+q^{7}+(1+\beta )q^{13}-q^{17}+(2+\cdots)q^{19}+\cdots\)
1512.2.a.o 1512.a 1.a $2$ $12.073$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(-2-\beta )q^{11}-2\beta q^{13}+\cdots\)
1512.2.a.p 1512.a 1.a $2$ $12.073$ \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}+(2-\beta )q^{11}+2\beta q^{13}+\cdots\)
1512.2.a.q 1512.a 1.a $2$ $12.073$ \(\Q(\sqrt{33}) \) None \(0\) \(0\) \(1\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}+q^{7}+(1+\beta )q^{13}+q^{17}+(2+\cdots)q^{19}+\cdots\)
1512.2.a.r 1512.a 1.a $2$ $12.073$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(4\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+q^{7}-3\beta q^{11}-2\beta q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1512))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1512)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(168))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(756))\)\(^{\oplus 2}\)