Properties

Label 1900.3.e
Level $1900$
Weight $3$
Character orbit 1900.e
Rep. character $\chi_{1900}(1101,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $8$
Sturm bound $900$
Trace bound $9$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(900\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1900, [\chi])\).

Total New Old
Modular forms 618 64 554
Cusp forms 582 64 518
Eisenstein series 36 0 36

Trace form

\( 64 q + 9 q^{7} - 202 q^{9} + O(q^{10}) \) \( 64 q + 9 q^{7} - 202 q^{9} - q^{11} - 19 q^{17} - 24 q^{19} + 58 q^{23} - 66 q^{39} - 45 q^{43} + 95 q^{47} + 353 q^{49} + 34 q^{57} - 125 q^{61} - 133 q^{63} + 137 q^{73} + 87 q^{77} + 516 q^{81} - 36 q^{83} - 438 q^{87} - 164 q^{93} - 173 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1900.3.e.a \(2\) \(51.771\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(-5\) \(q+(-1-3\beta )q^{7}+9q^{9}+(1-5\beta )q^{11}+\cdots\)
1900.3.e.b \(2\) \(51.771\) \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{3}+q^{7}-20q^{9}+14q^{11}+3\beta q^{13}+\cdots\)
1900.3.e.c \(4\) \(51.771\) \(\Q(\sqrt{6}, \sqrt{-14})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+\beta _{2}q^{7}-5q^{9}+4q^{11}-3\beta _{1}q^{13}+\cdots\)
1900.3.e.d \(4\) \(51.771\) \(\Q(\sqrt{3}, \sqrt{19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{7}+9q^{9}+(1-\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{17}+\cdots\)
1900.3.e.e \(12\) \(51.771\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+\beta _{8}q^{7}+(-6-\beta _{1}+\beta _{3}+\cdots)q^{9}+\cdots\)
1900.3.e.f \(12\) \(51.771\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(12\) \(q+\beta _{1}q^{3}+(1+\beta _{9})q^{7}+(-1+\beta _{2})q^{9}+\cdots\)
1900.3.e.g \(14\) \(51.771\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)
1900.3.e.h \(14\) \(51.771\) \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(4\) \(q+\beta _{1}q^{3}+\beta _{7}q^{7}+(-4+\beta _{2})q^{9}-\beta _{3}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)