Properties

Label 2300.2.c
Level $2300$
Weight $2$
Character orbit 2300.c
Rep. character $\chi_{2300}(1749,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $10$
Sturm bound $720$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2300 = 2^{2} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2300.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2300, [\chi])\).

Total New Old
Modular forms 378 32 346
Cusp forms 342 32 310
Eisenstein series 36 0 36

Trace form

\( 32 q - 20 q^{9} + O(q^{10}) \) \( 32 q - 20 q^{9} - 8 q^{11} - 4 q^{19} + 8 q^{21} + 36 q^{29} - 8 q^{31} - 32 q^{39} - 20 q^{41} - 16 q^{49} - 8 q^{51} + 16 q^{59} + 8 q^{69} + 48 q^{71} + 48 q^{79} - 36 q^{89} - 16 q^{91} + 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2300, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
2300.2.c.a 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-2iq^{7}-6q^{9}-3iq^{13}+\cdots\)
2300.2.c.b 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-4iq^{7}-6q^{9}+2q^{11}+5iq^{13}+\cdots\)
2300.2.c.c 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-iq^{7}-q^{9}-3q^{11}-5iq^{13}+\cdots\)
2300.2.c.d 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+4iq^{7}+2q^{9}-6q^{11}-iq^{13}+\cdots\)
2300.2.c.e 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{7}+2q^{9}-4q^{11}-iq^{13}+\cdots\)
2300.2.c.f 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2iq^{7}+2q^{9}-iq^{13}+6iq^{17}+\cdots\)
2300.2.c.g 2300.c 5.b $2$ $18.366$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}+6q^{11}+6iq^{13}-7iq^{17}+\cdots\)
2300.2.c.h 2300.c 5.b $4$ $18.366$ \(\Q(i, \sqrt{17})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{7}+(-2+\beta _{3})q^{9}+\cdots\)
2300.2.c.i 2300.c 5.b $6$ $18.366$ 6.0.6594624.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{4})q^{3}+2\beta _{1}q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)
2300.2.c.j 2300.c 5.b $8$ $18.366$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5})q^{7}+(-1+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2300, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2300, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)