Properties

Label 1900.2.s
Level $1900$
Weight $2$
Character orbit 1900.s
Rep. character $\chi_{1900}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $60$
Newform subspaces $5$
Sturm bound $600$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(600\)
Trace bound: \(9\)
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

\( 60 q + 30 q^{9} + O(q^{10}) \) \( 60 q + 30 q^{9} + 4 q^{11} - 4 q^{19} + 2 q^{21} + 16 q^{29} + 4 q^{31} - 20 q^{39} - 36 q^{41} - 52 q^{49} - 4 q^{51} - 30 q^{59} - 8 q^{61} - 56 q^{69} + 10 q^{71} + 8 q^{79} - 70 q^{81} + 50 q^{89} - 34 q^{91} + 4 q^{99} + O(q^{100}) \)

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.s.a \(4\) \(15.172\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{9}-4q^{11}+(-\zeta_{12}+\cdots)q^{13}+\cdots\)
1900.2.s.b \(4\) \(15.172\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-2\zeta_{12}^{3}q^{7}+\zeta_{12}^{2}q^{9}+\cdots\)
1900.2.s.c \(12\) \(15.172\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{6}+\beta _{11})q^{3}+(\beta _{10}+\beta _{11})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.s.d \(16\) \(15.172\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{3}+\beta _{14}q^{7}+(\beta _{4}-\beta _{5}+\beta _{10}+\cdots)q^{9}+\cdots\)
1900.2.s.e \(24\) \(15.172\) None \(0\) \(0\) \(0\) \(0\)

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

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