Properties

Label 1950.2.bc
Level $1950$
Weight $2$
Character orbit 1950.bc
Rep. character $\chi_{1950}(751,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $88$
Newform subspaces $11$
Sturm bound $840$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 11 \)
Sturm bound: \(840\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1950, [\chi])\).

Total New Old
Modular forms 888 88 800
Cusp forms 792 88 704
Eisenstein series 96 0 96

Trace form

\( 88q + 44q^{4} - 44q^{9} + O(q^{10}) \) \( 88q + 44q^{4} - 44q^{9} - 24q^{11} + 12q^{13} - 44q^{16} - 8q^{17} + 36q^{19} + 8q^{23} - 20q^{26} - 20q^{29} - 12q^{33} + 44q^{36} - 12q^{37} + 16q^{39} + 12q^{41} - 4q^{42} + 8q^{43} + 24q^{46} + 32q^{49} + 16q^{53} + 36q^{58} + 24q^{59} + 16q^{61} + 8q^{62} - 88q^{64} - 24q^{66} + 24q^{67} + 8q^{68} - 4q^{69} + 72q^{71} + 28q^{74} + 36q^{76} + 32q^{77} + 40q^{79} - 44q^{81} + 12q^{82} - 24q^{84} + 12q^{87} + 48q^{89} - 36q^{91} + 16q^{92} - 24q^{93} + 16q^{94} - 72q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1950, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1950.2.bc.a \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1950.2.bc.b \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
1950.2.bc.c \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(-2\) \(0\) \(6\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}-\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1950.2.bc.d \(4\) \(15.571\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(0\) \(-6\) \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+(1+\cdots)q^{4}+\cdots\)
1950.2.bc.e \(8\) \(15.571\) \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(0\) \(0\) \(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}-\zeta_{24}^{4}q^{3}+(1+\cdots)q^{4}+\cdots\)
1950.2.bc.f \(8\) \(15.571\) \(\Q(\zeta_{24})\) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{24}^{2}q^{2}+(1-\zeta_{24}^{4})q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
1950.2.bc.g \(8\) \(15.571\) 8.0.\(\cdots\).1 None \(0\) \(4\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{5})q^{2}+(1-\beta _{6})q^{3}+\beta _{6}q^{4}+\cdots\)
1950.2.bc.h \(12\) \(15.571\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(0\) \(-6\) \(q-\beta _{8}q^{2}-\beta _{4}q^{3}+(1-\beta _{4})q^{4}+\beta _{9}q^{6}+\cdots\)
1950.2.bc.i \(12\) \(15.571\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(0\) \(12\) \(q+(\beta _{4}+\beta _{7})q^{2}+\beta _{6}q^{3}+(1+\beta _{6})q^{4}+\cdots\)
1950.2.bc.j \(12\) \(15.571\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(6\) \(0\) \(-12\) \(q+(-\beta _{4}-\beta _{7})q^{2}-\beta _{6}q^{3}+(1+\beta _{6}+\cdots)q^{4}+\cdots\)
1950.2.bc.k \(12\) \(15.571\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(6\) \(0\) \(6\) \(q+\beta _{8}q^{2}+\beta _{4}q^{3}+(1-\beta _{4})q^{4}+\beta _{9}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1950, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)