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Properties

Label 1900.2.a
Level $1900$
Weight $2$
Character orbit 1900.a
Rep. character $\chi_{1900}(1,\cdot)$
Character field $\Q$
Dimension $29$
Newform subspaces $11$
Sturm bound $600$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(600\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1900))\).

Total New Old
Modular forms 318 29 289
Cusp forms 283 29 254
Eisenstein series 35 0 35

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

\(2\)\(5\)\(19\)FrickeDim
\(-\)\(+\)\(+\)$-$\(7\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(7\)
\(-\)\(-\)\(-\)$-$\(9\)
Plus space\(+\)\(13\)
Minus space\(-\)\(16\)

Trace form

\( 29 q - 2 q^{3} + 3 q^{7} + 29 q^{9} + O(q^{10}) \) \( 29 q - 2 q^{3} + 3 q^{7} + 29 q^{9} - q^{11} + 8 q^{13} - q^{17} + q^{19} + 2 q^{21} + 8 q^{23} + 16 q^{27} - 18 q^{29} + 8 q^{31} - 6 q^{33} - 2 q^{37} - 4 q^{39} - 10 q^{41} - 9 q^{43} - 7 q^{47} + 36 q^{49} + 10 q^{51} + 4 q^{53} - 2 q^{57} - 14 q^{59} - 3 q^{61} - 29 q^{63} + 8 q^{67} + 16 q^{69} + 22 q^{71} + 3 q^{73} - q^{77} - 8 q^{79} + 41 q^{81} + 4 q^{83} - 20 q^{87} + 20 q^{89} - 32 q^{91} - 32 q^{93} + 24 q^{97} + 51 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1900))\) 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 5 19
1900.2.a.a 1900.a 1.a $1$ $15.172$ \(\Q\) None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{7}+q^{9}-6q^{13}-2q^{17}+\cdots\)
1900.2.a.b 1900.a 1.a $1$ $15.172$ \(\Q\) None \(0\) \(-2\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+3q^{7}+q^{9}+5q^{11}+4q^{13}+\cdots\)
1900.2.a.c 1900.a 1.a $1$ $15.172$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-4q^{11}+4q^{13}-6q^{17}+\cdots\)
1900.2.a.d 1900.a 1.a $2$ $15.172$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-2q^{7}+(1-2\beta )q^{9}+\cdots\)
1900.2.a.e 1900.a 1.a $2$ $15.172$ \(\Q(\sqrt{2}) \) None \(0\) \(4\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+(2-2\beta )q^{7}+(3+4\beta )q^{9}+\cdots\)
1900.2.a.f 1900.a 1.a $3$ $15.172$ 3.3.257.1 None \(0\) \(-2\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1})q^{7}+(1+\cdots)q^{9}+\cdots\)
1900.2.a.g 1900.a 1.a $3$ $15.172$ 3.3.321.1 None \(0\) \(-2\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2})q^{7}+\cdots\)
1900.2.a.h 1900.a 1.a $3$ $15.172$ 3.3.257.1 None \(0\) \(2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{1})q^{7}+(1-2\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.a.i 1900.a 1.a $3$ $15.172$ 3.3.321.1 None \(0\) \(2\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(1-2\beta _{1}-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\)
1900.2.a.j 1900.a 1.a $4$ $15.172$ \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
1900.2.a.k 1900.a 1.a $6$ $15.172$ 6.6.56310016.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}-\beta _{4}q^{7}+(2-\beta _{1}+\beta _{5})q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 2}\)