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Properties

Label 1452.2.a
Level $1452$
Weight $2$
Character orbit 1452.a
Rep. character $\chi_{1452}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $13$
Sturm bound $528$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1452.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(528\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1452))\).

Total New Old
Modular forms 300 18 282
Cusp forms 229 18 211
Eisenstein series 71 0 71

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

\(2\)\(3\)\(11\)FrickeDim
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(5\)
\(-\)\(-\)\(+\)$+$\(2\)
\(-\)\(-\)\(-\)$-$\(7\)
Plus space\(+\)\(7\)
Minus space\(-\)\(11\)

Trace form

\( 18 q - 4 q^{5} + 18 q^{9} + O(q^{10}) \) \( 18 q - 4 q^{5} + 18 q^{9} - 4 q^{13} + 8 q^{19} + 4 q^{21} + 12 q^{23} + 22 q^{25} + 8 q^{29} + 12 q^{31} + 8 q^{39} - 8 q^{41} - 8 q^{43} - 4 q^{45} + 8 q^{47} + 26 q^{49} - 8 q^{51} - 16 q^{53} + 4 q^{57} - 4 q^{59} + 4 q^{61} - 8 q^{65} - 12 q^{67} - 4 q^{69} - 4 q^{71} - 12 q^{73} + 8 q^{75} + 18 q^{81} - 32 q^{83} + 8 q^{87} + 28 q^{89} + 28 q^{91} + 44 q^{93} + 16 q^{95} + 48 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1452))\) 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 11
1452.2.a.a 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(-1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{7}+q^{9}+3q^{13}+q^{15}+\cdots\)
1452.2.a.b 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(-1\) \(-1\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+2q^{7}+q^{9}-3q^{13}+q^{15}+\cdots\)
1452.2.a.c 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(-1\) \(2\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-2q^{7}+q^{9}-6q^{13}+\cdots\)
1452.2.a.d 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(1\) \(-4\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-5q^{7}+q^{9}-2q^{13}+\cdots\)
1452.2.a.e 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(1\) \(-4\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}+5q^{7}+q^{9}+2q^{13}+\cdots\)
1452.2.a.f 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(1\) \(2\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
1452.2.a.g 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(1\) \(3\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}-2q^{7}+q^{9}-5q^{13}+\cdots\)
1452.2.a.h 1452.a 1.a $1$ $11.594$ \(\Q\) None \(0\) \(1\) \(3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+2q^{7}+q^{9}+5q^{13}+\cdots\)
1452.2.a.i 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-3\beta )q^{5}+(-3+2\beta )q^{7}+\cdots\)
1452.2.a.j 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-1\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+(1-3\beta )q^{5}+(3-2\beta )q^{7}+q^{9}+\cdots\)
1452.2.a.k 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-\beta q^{7}+q^{9}+\beta q^{19}+\beta q^{21}+\cdots\)
1452.2.a.l 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-1\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+(-3+2\beta )q^{7}+q^{9}+\cdots\)
1452.2.a.m 1452.a 1.a $2$ $11.594$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-\beta q^{5}+(3-2\beta )q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1452))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1452)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)