Properties

Label 1900.2.i
Level $1900$
Weight $2$
Character orbit 1900.i
Rep. character $\chi_{1900}(201,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $62$
Newform subspaces $7$
Sturm bound $600$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(600\)
Trace bound: \(3\)
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 62 574
Cusp forms 564 62 502
Eisenstein series 72 0 72

Trace form

\( 62q + q^{3} + 4q^{7} - 28q^{9} + O(q^{10}) \) \( 62q + q^{3} + 4q^{7} - 28q^{9} + 4q^{11} - 7q^{13} + q^{17} - 12q^{19} - 6q^{21} - 5q^{23} - 2q^{27} + 9q^{29} + 12q^{31} - 12q^{33} + 36q^{37} + 54q^{39} + q^{41} - 17q^{43} - 23q^{47} + 78q^{49} + 35q^{51} - 13q^{53} - 35q^{57} + 11q^{59} - 7q^{61} - 6q^{63} - 13q^{67} - 34q^{69} + 11q^{71} + 13q^{73} - 20q^{77} + 13q^{79} - 7q^{81} + 20q^{83} + 26q^{87} + 7q^{89} - 18q^{91} + 19q^{97} + O(q^{100}) \)

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.i.a \(2\) \(15.172\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(0\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{9}-4q^{11}+\cdots\)
1900.2.i.b \(2\) \(15.172\) \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(0\) \(8\) \(q+(2-2\zeta_{6})q^{3}+4q^{7}-\zeta_{6}q^{9}-3q^{11}+\cdots\)
1900.2.i.c \(6\) \(15.172\) 6.0.1783323.2 None \(0\) \(-1\) \(0\) \(-4\) \(q+(-\beta _{3}+\beta _{5})q^{3}+(-1+\beta _{3})q^{7}+(\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.d \(8\) \(15.172\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(1\) \(0\) \(0\) \(q+\beta _{1}q^{3}-\beta _{7}q^{7}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
1900.2.i.e \(12\) \(15.172\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-3\) \(0\) \(0\) \(q+(-1+\beta _{1}-\beta _{6})q^{3}+\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.f \(12\) \(15.172\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(0\) \(0\) \(q+(1-\beta _{1}+\beta _{6})q^{3}-\beta _{4}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1900.2.i.g \(20\) \(15.172\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{14}q^{3}+(\beta _{15}+\beta _{18})q^{7}+(-1+\beta _{4}+\cdots)q^{9}+\cdots\)

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

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