Properties

Label 1950.2.b
Level $1950$
Weight $2$
Character orbit 1950.b
Rep. character $\chi_{1950}(1351,\cdot)$
Character field $\Q$
Dimension $42$
Newform subspaces $13$
Sturm bound $840$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 13 \)
Sturm bound: \(840\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(7\), \(11\), \(17\), \(19\)

Dimensions

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

Total New Old
Modular forms 444 42 402
Cusp forms 396 42 354
Eisenstein series 48 0 48

Trace form

\( 42 q + 2 q^{3} - 42 q^{4} + 42 q^{9} - 2 q^{12} + 2 q^{13} - 12 q^{14} + 42 q^{16} - 4 q^{17} - 8 q^{23} + 8 q^{26} + 2 q^{27} - 28 q^{29} - 42 q^{36} + 12 q^{38} - 18 q^{39} + 4 q^{42} - 24 q^{43} + 2 q^{48}+ \cdots - 40 q^{94}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1950.2.b.a 1950.b 13.b $2$ $15.571$ \(\Q(\sqrt{-1}) \) None 1950.2.b.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}-q^{3}-q^{4}+i q^{6}+2 i q^{7}+\cdots\)
1950.2.b.b 1950.b 13.b $2$ $15.571$ \(\Q(\sqrt{-1}) \) None 1950.2.b.b \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-q^{3}-q^{4}-i q^{6}+3 i q^{7}+\cdots\)
1950.2.b.c 1950.b 13.b $2$ $15.571$ \(\Q(\sqrt{-1}) \) None 78.2.b.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}-q^{3}-q^{4}+i q^{6}+2 i q^{7}+\cdots\)
1950.2.b.d 1950.b 13.b $2$ $15.571$ \(\Q(\sqrt{-1}) \) None 1950.2.b.b \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+q^{3}-q^{4}+i q^{6}+3 i q^{7}+\cdots\)
1950.2.b.e 1950.b 13.b $2$ $15.571$ \(\Q(\sqrt{-1}) \) None 390.2.b.b \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}+q^{3}-q^{4}-i q^{6}+i q^{8}+\cdots\)
1950.2.b.f 1950.b 13.b $2$ $15.571$ \(\Q(\sqrt{-1}) \) None 1950.2.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-i q^{2}+q^{3}-q^{4}-i q^{6}+2 i q^{7}+\cdots\)
1950.2.b.g 1950.b 13.b $2$ $15.571$ \(\Q(\sqrt{-1}) \) None 390.2.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+q^{3}-q^{4}+i q^{6}-i q^{8}+\cdots\)
1950.2.b.h 1950.b 13.b $4$ $15.571$ \(\Q(i, \sqrt{17})\) None 390.2.b.d \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.2.b.i 1950.b 13.b $4$ $15.571$ \(\Q(i, \sqrt{17})\) None 1950.2.b.i \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{3}-q^{4}-\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
1950.2.b.j 1950.b 13.b $4$ $15.571$ \(\Q(i, \sqrt{17})\) None 1950.2.b.i \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{6}+(\beta _{1}+3\beta _{2}+\cdots)q^{7}+\cdots\)
1950.2.b.k 1950.b 13.b $4$ $15.571$ \(\Q(i, \sqrt{13})\) None 390.2.b.c \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1950.2.b.l 1950.b 13.b $6$ $15.571$ 6.0.350464.1 None 390.2.f.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-q^{3}-q^{4}-\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
1950.2.b.m 1950.b 13.b $6$ $15.571$ 6.0.350464.1 None 390.2.f.a \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+q^{3}-q^{4}+\beta _{4}q^{6}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1950, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(650, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(975, [\chi])\)\(^{\oplus 2}\)