Properties

Label 1950.2.e
Level $1950$
Weight $2$
Character orbit 1950.e
Rep. character $\chi_{1950}(1249,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $16$
Sturm bound $840$
Trace bound $19$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 16 \)
Sturm bound: \(840\)
Trace bound: \(19\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(31\)

Dimensions

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

Total New Old
Modular forms 444 36 408
Cusp forms 396 36 360
Eisenstein series 48 0 48

Trace form

\( 36q - 36q^{4} + 4q^{6} - 36q^{9} + O(q^{10}) \) \( 36q - 36q^{4} + 4q^{6} - 36q^{9} + 16q^{11} + 36q^{16} - 8q^{19} + 8q^{21} - 4q^{24} + 16q^{29} - 24q^{31} - 16q^{34} + 36q^{36} - 32q^{41} - 16q^{44} + 32q^{46} - 12q^{49} - 16q^{51} - 4q^{54} + 32q^{61} - 36q^{64} + 16q^{69} - 32q^{71} + 32q^{74} + 8q^{76} - 8q^{79} + 36q^{81} - 8q^{84} - 64q^{86} - 16q^{89} - 8q^{91} + 32q^{94} + 4q^{96} - 16q^{99} + O(q^{100}) \)

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.e.a \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
1950.2.e.b \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{7}+iq^{8}+\cdots\)
1950.2.e.c \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1950.2.e.d \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1950.2.e.e \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+4iq^{7}+\cdots\)
1950.2.e.f \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+2iq^{7}+\cdots\)
1950.2.e.g \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
1950.2.e.h \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-iq^{8}-q^{9}+\cdots\)
1950.2.e.i \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1950.2.e.j \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+3iq^{7}+\cdots\)
1950.2.e.k \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1950.2.e.l \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{8}-q^{9}+\cdots\)
1950.2.e.m \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}+2iq^{7}+\cdots\)
1950.2.e.n \(2\) \(15.571\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}+iq^{3}-q^{4}+q^{6}+4iq^{7}+\cdots\)
1950.2.e.o \(4\) \(15.571\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}q^{3}-q^{4}+q^{6}+\zeta_{8}^{2}q^{7}+\cdots\)
1950.2.e.p \(4\) \(15.571\) \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+\beta _{2}q^{3}-q^{4}+q^{6}+(\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)