Properties

Label 1900.2.c
Level $1900$
Weight $2$
Character orbit 1900.c
Rep. character $\chi_{1900}(1749,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $7$
Sturm bound $600$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(600\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1900, [\chi])\).

Total New Old
Modular forms 318 26 292
Cusp forms 282 26 256
Eisenstein series 36 0 36

Trace form

\( 26 q - 26 q^{9} + O(q^{10}) \) \( 26 q - 26 q^{9} - 10 q^{11} + 2 q^{19} + 8 q^{21} + 20 q^{29} + 12 q^{31} - 44 q^{39} - 20 q^{49} - 32 q^{51} + 12 q^{59} - 30 q^{61} - 40 q^{69} + 20 q^{71} + 48 q^{79} + 42 q^{81} - 44 q^{89} - 36 q^{91} + 38 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1900, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1900.2.c.a 1900.c 5.b $2$ $15.172$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}+3iq^{13}-iq^{17}+\cdots\)
1900.2.c.b 1900.c 5.b $2$ $15.172$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+3iq^{7}-q^{9}+5q^{11}-4iq^{13}+\cdots\)
1900.2.c.c 1900.c 5.b $2$ $15.172$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+3q^{9}-4q^{11}+2iq^{13}+3iq^{17}+\cdots\)
1900.2.c.d 1900.c 5.b $4$ $15.172$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{2})q^{3}+(-\zeta_{8}-2\zeta_{8}^{2})q^{7}+\cdots\)
1900.2.c.e 1900.c 5.b $4$ $15.172$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}+\zeta_{12}^{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
1900.2.c.f 1900.c 5.b $6$ $15.172$ 6.0.6594624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1900.2.c.g 1900.c 5.b $6$ $15.172$ 6.0.4227136.2 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{1}q^{7}+\beta _{5}q^{9}-\beta _{2}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(475, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(950, [\chi])\)\(^{\oplus 2}\)