Properties

Label 48.19.e
Level $48$
Weight $19$
Character orbit 48.e
Rep. character $\chi_{48}(17,\cdot)$
Character field $\Q$
Dimension $35$
Newform subspaces $5$
Sturm bound $152$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 19 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(152\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(48, [\chi])\).

Total New Old
Modular forms 150 37 113
Cusp forms 138 35 103
Eisenstein series 12 2 10

Trace form

\( 35 q + q^{3} + 12907082 q^{7} + 45299419 q^{9} + O(q^{10}) \) \( 35 q + q^{3} + 12907082 q^{7} + 45299419 q^{9} - 2 q^{13} + 22984127968 q^{15} - 576437493022 q^{19} + 518159703918 q^{21} - 25097288426389 q^{25} + 5577774140809 q^{27} + 49274776084250 q^{31} + 5044028223008 q^{33} + 29131241006734 q^{37} + 184709334187498 q^{39} + 1347253979686130 q^{43} + 368309837890624 q^{45} + 4938591669474201 q^{49} - 7671120832100224 q^{51} - 11938872988195776 q^{55} - 8274568254971786 q^{57} - 7965447864377186 q^{61} + 39841635854926938 q^{63} + 22097064221576066 q^{67} - 5424718908675136 q^{69} - 9565993799943626 q^{73} - 80914930191059431 q^{75} - 70300521673683910 q^{79} - 104612698789882349 q^{81} + 59020027563684096 q^{85} - 191137374834968160 q^{87} - 1283027325185819228 q^{91} + 431894702490376030 q^{93} - 565789518330828410 q^{97} + 2441943244522877888 q^{99} + O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(48, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
48.19.e.a 48.e 3.b $1$ $98.585$ \(\Q\) \(\Q(\sqrt{-3}) \) 3.19.b.a \(0\) \(19683\) \(0\) \(-77549186\) $\mathrm{U}(1)[D_{2}]$ \(q+3^{9}q^{3}-77549186q^{7}+3^{18}q^{9}+\cdots\)
48.19.e.b 48.e 3.b $4$ $98.585$ 4.0.601940665.1 None 3.19.b.b \(0\) \(-15876\) \(0\) \(95744152\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-63^{2}+\beta _{1}+\beta _{2})q^{3}+(-45\beta _{1}+\cdots)q^{5}+\cdots\)
48.19.e.c 48.e 3.b $6$ $98.585$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None 12.19.c.a \(0\) \(-23934\) \(0\) \(-11024364\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3989+\beta _{1})q^{3}+(-4\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
48.19.e.d 48.e 3.b $6$ $98.585$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 6.19.b.a \(0\) \(6258\) \(0\) \(-28233804\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1043-\beta _{1})q^{3}+(-46\beta _{1}-19\beta _{2}+\cdots)q^{5}+\cdots\)
48.19.e.e 48.e 3.b $18$ $98.585$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None 24.19.e.a \(0\) \(13870\) \(0\) \(33970284\) $\mathrm{SU}(2)[C_{2}]$ \(q+(771-\beta _{1})q^{3}+(-4+9\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{19}^{\mathrm{old}}(48, [\chi])\) into lower level spaces

\( S_{19}^{\mathrm{old}}(48, [\chi]) \simeq \) \(S_{19}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)