Properties

Label 1900.2.l
Level $1900$
Weight $2$
Character orbit 1900.l
Rep. character $\chi_{1900}(493,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $60$
Newform subspaces $4$
Sturm bound $600$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(600\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 636 60 576
Cusp forms 564 60 504
Eisenstein series 72 0 72

Trace form

\( 60q + 2q^{7} + O(q^{10}) \) \( 60q + 2q^{7} - 16q^{11} - 10q^{17} - 20q^{23} + 26q^{43} + 6q^{47} - 24q^{57} + 8q^{61} - 2q^{63} + 54q^{73} - 10q^{77} + 36q^{81} - 20q^{83} + 80q^{87} - 8q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1900.2.l.a \(8\) \(15.172\) 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(6\) \(q+(1+\beta _{1}+\beta _{5})q^{7}-3\beta _{1}q^{9}+(-1+\cdots)q^{11}+\cdots\)
1900.2.l.b \(12\) \(15.172\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta _{2}q^{3}-\beta _{6}q^{7}+(\beta _{3}+4\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots\)
1900.2.l.c \(16\) \(15.172\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{3}+\beta _{9}q^{7}+(-\beta _{2}-\beta _{11})q^{9}+\cdots\)
1900.2.l.d \(24\) \(15.172\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1900, [\chi])\) into lower level spaces

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