Properties

Label 1900.3.g
Level $1900$
Weight $3$
Character orbit 1900.g
Rep. character $\chi_{1900}(949,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $4$
Sturm bound $900$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(900\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 618 60 558
Cusp forms 582 60 522
Eisenstein series 36 0 36

Trace form

\( 60q + 180q^{9} + O(q^{10}) \) \( 60q + 180q^{9} - 6q^{11} + 46q^{19} + 212q^{39} - 378q^{49} - 162q^{61} + 76q^{81} + 206q^{99} + O(q^{100}) \)

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.g.a \(4\) \(51.771\) \(\Q(i, \sqrt{57})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+(2\beta _{1}+\beta _{2})q^{7}-9q^{9}+(-2+\beta _{3})q^{11}+\cdots\)
1900.3.g.b \(4\) \(51.771\) \(\Q(i, \sqrt{29})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{3}-\beta _{1}q^{7}+20q^{9}+14q^{11}+\cdots\)
1900.3.g.c \(24\) \(51.771\) None \(0\) \(0\) \(0\) \(0\)
1900.3.g.d \(28\) \(51.771\) None \(0\) \(0\) \(0\) \(0\)

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

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