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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1900.2.l.a 1900.l 95.g $8$ $15.172$ 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(6\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{1}+\beta _{5})q^{7}-3\beta _{1}q^{9}+(-1+\cdots)q^{11}+\cdots\)
1900.2.l.b 1900.l 95.g $12$ $15.172$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}-\beta _{6}q^{7}+(\beta _{3}+4\beta _{5}-\beta _{6}+\cdots)q^{9}+\cdots\)
1900.2.l.c 1900.l 95.g $16$ $15.172$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{3}+\beta _{9}q^{7}+(-\beta _{2}-\beta _{11})q^{9}+\cdots\)
1900.2.l.d 1900.l 95.g $24$ $15.172$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

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