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Properties

Label 1444.2.a
Level $1444$
Weight $2$
Character orbit 1444.a
Rep. character $\chi_{1444}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $9$
Sturm bound $380$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1444 = 2^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1444.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(380\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1444))\).

Total New Old
Modular forms 220 29 191
Cusp forms 161 29 132
Eisenstein series 59 0 59

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

\(2\)\(19\)FrickeDim
\(-\)\(+\)$-$\(17\)
\(-\)\(-\)$+$\(12\)
Plus space\(+\)\(12\)
Minus space\(-\)\(17\)

Trace form

\( 29 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 29 q^{9} + O(q^{10}) \) \( 29 q - 2 q^{3} + 2 q^{5} + 4 q^{7} + 29 q^{9} - 4 q^{11} + 4 q^{13} + 2 q^{15} + 4 q^{17} + 6 q^{21} - 10 q^{23} + 35 q^{25} + 4 q^{27} + 2 q^{29} - 4 q^{31} - 10 q^{33} - 4 q^{35} - 10 q^{37} + 2 q^{39} - 10 q^{41} + 4 q^{43} + 6 q^{45} - 4 q^{47} + 33 q^{49} + 6 q^{51} + 4 q^{53} + 8 q^{55} - 6 q^{59} + 10 q^{61} + 2 q^{63} - 4 q^{65} + 12 q^{67} - 16 q^{69} - 2 q^{71} - 8 q^{73} + 8 q^{75} + 14 q^{77} - 8 q^{79} + 45 q^{81} + 14 q^{83} + 2 q^{87} - 12 q^{89} - 12 q^{91} - 8 q^{93} + 8 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1444))\) 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 19
1444.2.a.a 1444.a 1.a $1$ $11.530$ \(\Q\) None \(0\) \(-2\) \(-1\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)
1444.2.a.b 1444.a 1.a $1$ $11.530$ \(\Q\) None \(0\) \(-1\) \(-1\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-2q^{9}-4q^{11}-q^{13}+\cdots\)
1444.2.a.c 1444.a 1.a $1$ $11.530$ \(\Q\) None \(0\) \(1\) \(-1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-2q^{9}-4q^{11}+q^{13}+\cdots\)
1444.2.a.d 1444.a 1.a $2$ $11.530$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-2\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2\beta q^{5}+(1+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
1444.2.a.e 1444.a 1.a $2$ $11.530$ \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(1\) \(-3\) $-$ $+$ $N(\mathrm{U}(1))$ \(q+\beta q^{5}+(-2+\beta )q^{7}-3q^{9}+(2+\beta )q^{11}+\cdots\)
1444.2.a.f 1444.a 1.a $2$ $11.530$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-2\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2\beta q^{5}+(1+2\beta )q^{7}+(-2+\cdots)q^{9}+\cdots\)
1444.2.a.g 1444.a 1.a $6$ $11.530$ 6.6.20319417.1 None \(0\) \(-3\) \(-3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1444.2.a.h 1444.a 1.a $6$ $11.530$ 6.6.20319417.1 None \(0\) \(3\) \(-3\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1444.2.a.i 1444.a 1.a $8$ $11.530$ 8.8.\(\cdots\).1 None \(0\) \(0\) \(14\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{3}+\beta _{5})q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(2+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1444))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1444)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(722))\)\(^{\oplus 2}\)