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Properties

Label 1900.4.a
Level $1900$
Weight $4$
Character orbit 1900.a
Rep. character $\chi_{1900}(1,\cdot)$
Character field $\Q$
Dimension $85$
Newform subspaces $13$
Sturm bound $1200$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1900.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(1200\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(1900))\).

Total New Old
Modular forms 918 85 833
Cusp forms 882 85 797
Eisenstein series 36 0 36

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
\(-\)\(+\)\(+\)$-$\(20\)
\(-\)\(+\)\(-\)$+$\(21\)
\(-\)\(-\)\(+\)$+$\(23\)
\(-\)\(-\)\(-\)$-$\(21\)
Plus space\(+\)\(44\)
Minus space\(-\)\(41\)

Trace form

\( 85 q + 4 q^{3} - 14 q^{7} + 775 q^{9} + O(q^{10}) \) \( 85 q + 4 q^{3} - 14 q^{7} + 775 q^{9} - 48 q^{11} + 30 q^{13} + 86 q^{17} - 19 q^{19} - 88 q^{21} - 162 q^{23} - 32 q^{27} + 198 q^{29} + 164 q^{31} - 92 q^{33} - 10 q^{37} - 186 q^{39} + 510 q^{41} + 564 q^{43} + 216 q^{47} + 3993 q^{49} + 1216 q^{51} - 1154 q^{53} + 114 q^{57} - 188 q^{59} - 780 q^{61} + 1124 q^{63} - 1652 q^{67} + 140 q^{69} - 1340 q^{71} + 1842 q^{73} + 1118 q^{77} + 1916 q^{79} + 4213 q^{81} + 580 q^{83} + 1294 q^{87} - 5298 q^{89} - 448 q^{91} + 476 q^{93} - 678 q^{97} - 1100 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(1900))\) 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
1900.4.a.a 1900.a 1.a $1$ $112.104$ \(\Q\) None \(0\) \(-1\) \(0\) \(-19\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-19q^{7}-26q^{9}+20q^{11}+77q^{13}+\cdots\)
1900.4.a.b 1900.a 1.a $2$ $112.104$ \(\Q(\sqrt{33}) \) None \(0\) \(5\) \(0\) \(30\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(3-\beta )q^{3}+(17-4\beta )q^{7}+(-10-5\beta )q^{9}+\cdots\)
1900.4.a.c 1900.a 1.a $3$ $112.104$ 3.3.35529.1 None \(0\) \(-1\) \(0\) \(-44\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{3}+(-15+\beta _{1}+2\beta _{2})q^{7}+\cdots\)
1900.4.a.d 1900.a 1.a $4$ $112.104$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(-7\) \(0\) \(-23\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{3}+(-6-\beta _{1}-\beta _{2}+\beta _{3})q^{7}+\cdots\)
1900.4.a.e 1900.a 1.a $4$ $112.104$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(2\) \(0\) \(28\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(8+\beta _{1}-\beta _{2})q^{7}+(5^{2}-2\beta _{1}+\cdots)q^{9}+\cdots\)
1900.4.a.f 1900.a 1.a $4$ $112.104$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(11\) \(0\) \(33\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(3-\beta _{2})q^{3}+(8-\beta _{1}-\beta _{3})q^{7}+(9+\cdots)q^{9}+\cdots\)
1900.4.a.g 1900.a 1.a $5$ $112.104$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-5\) \(0\) \(-19\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+(-4-\beta _{1}-\beta _{4})q^{7}+\cdots\)
1900.4.a.h 1900.a 1.a $9$ $112.104$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-6\) \(0\) \(-14\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-2-\beta _{4})q^{7}+(11+\cdots)q^{9}+\cdots\)
1900.4.a.i 1900.a 1.a $9$ $112.104$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-6\) \(0\) \(-14\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{5})q^{7}+\cdots\)
1900.4.a.j 1900.a 1.a $9$ $112.104$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(6\) \(0\) \(14\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(2+\beta _{4})q^{7}+(11-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.4.a.k 1900.a 1.a $9$ $112.104$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(6\) \(0\) \(14\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1+\beta _{1}+\beta _{5})q^{7}+(15+\cdots)q^{9}+\cdots\)
1900.4.a.l 1900.a 1.a $12$ $112.104$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{11}q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
1900.4.a.m 1900.a 1.a $14$ $112.104$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{9}q^{7}+(6+\beta _{2})q^{9}+(2-\beta _{5}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(1900))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(1900)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(950))\)\(^{\oplus 2}\)